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I don't think you can get there in a single movement, Vuldruk. Your profile isn't complete, but it does indicate you are wearing scale armor, which would reduce your speed by 10 feet. With barbarian fast movement, that's 30 feet move speed. The square you moved to is 35 feet away from your previous location (remember that the second diagonal is 10 feet). Do you have a feat or feature that gives you more movement than that?

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The further thug runs up and attacks Pau, trying to bean him with a bag of lead balls. He gets a lucky shot in and rings the monk's bell. 14 nonlethal damage to Pau with a confirmed crit.
The other thug, wheezing from the monk's punch, tries to dodge away from the fight. However, Pau sees him and manages a lucky stike, knocking him out. Yellow is unconscious.
Kura, badly hurt, tosses a tanglefoot bag at Arin, then ducks behind the edge of the roof to hide. The bag of sticky tar hits Arin's armor and bursts all over her, but she manages to react quickly enough to keep from being stuck to the ground. Arin is entangled, but not immobilized, for 3 rounds. Please look up the condition and apply it to your attacks and other rolls.
All PCs are up!
sap attack: 1d20 + 4 ⇒ (20) + 4 = 24
confirm: 1d20 + 4 ⇒ (14) + 4 = 18
damage: 2d6 + 4 ⇒ (5, 5) + 4 = 14
acrobatics: 1d20 + 7 ⇒ (7) + 7 = 14
Pau AoO: 1d20 + 8 ⇒ (14) + 8 = 22
1d8 + 5 ⇒ (3) + 5 = 8
touch attack vs. Arin: 1d20 + 2 ⇒ (12) + 2 = 14
2d4 ⇒ (2, 1) = 3
Arin Reflex: 1d20 + 3 ⇒ (19) + 3 = 22

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Telos wheels around Telka to further put teammates between him and the foes.
15', move action
Again he sends an electric ray up over the roof at the woman.
Elemental ray vs boss-woman touch AC, blessed: 1d20 + 6 + 1 ⇒ (9) + 6 + 1 = 16
Electricity damage: 1d6 + 1 ⇒ (4) + 1 = 5

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She's almost completely hidden behind the roof (improved cover) so that misses.

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Pau kicks and punches the new opponent that cracked him in the skull.
Attack 1d20 + 7 ⇒ (19) + 7 = 26
Damage 1d8 + 5 ⇒ (1) + 5 = 6
Attack 1d20 + 7 ⇒ (4) + 7 = 11
Damage 1d8 + 5 ⇒ (1) + 5 = 6

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-2 to attack, -4 to DEX, move at half speed
"Damn that woman!" Arin mutters as she tries to clear some of the goo off her bow. She fires another arrow at the woman, more in frustration than anything else.
bow: 1d20 + 5 - 3 ⇒ (19) + 5 - 3 = 21 damage: 1d8 + 1 ⇒ (8) + 1 = 9
"Don't let her get away!" she hollers, hoping some of her allies can still hear her and might cut off any escape routes.

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Telak taps Arin on the shoulder, Desna's blessings be upon ye lass he says before jogging over to help Pau.
Using Bit of Luck on Arin, roll twice for all d20 rolls until the end of your next turn. Then moving 25'
Dont worry Pau, I'll help you deal with this ruffian!
Pau, if you wait on your next turn I will bit of luck you and get into a flanking position.

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Vuldruk strikes down the remaining thug. Kura sees this and decides to make a run for it.
Acrobatics to jump down safely: 1d20 + 6 ⇒ (11) + 6 = 17
I've added more area to the tactical map so you have a chance of chasing her down. All PCs are up.

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Telos takes off in a dead run after her, trying to catch up and possibly getting behind her so the group can surround her...
60', straight line running for full round

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Still significantly tied up for the moment, Arin tries to shoot the fleeing assassin.
using bit of luck
bow: 1d20 + 5 - 3 ⇒ (2) + 5 - 3 = 4 or
bow: 1d20 + 5 - 3 ⇒ (7) + 5 - 3 = 9
damage: 1d8 + 1 ⇒ (1) + 1 = 2
no luck for me

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Using his 40’ movement, Pau takes off after the fleeing enemies.
If I can make a run action, that’d be 160’ I think. Could someone move me on the map, please?

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You're fast enough to get in front of her with a double move. Do you want to do that? She would get an attack of opportunity against you.

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Telka draws on his Desna granted speed and jogs up to them woman, Stand still and talk to us, we don't want to have to hurt you

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Kura clumsily stabs at Pau as he passes her, but nearly drops her blade. Seeing that she is trapped, she throws down her sword and cries out, "Fine, you got me! I give up!"
AoO: 1d20 + 1 ⇒ (1) + 1 = 2

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Good, you have decided to be sensible. Tell us who you are and why you attacked us
Diplomacy: 1d20 + 6 ⇒ (12) + 6 = 18

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"Just a case of mistaken identity. Thought you were some criminals needing to be captured. See, I was using nonlethal means!"
Searching her indicates she has a sap, a short sword, an alchemy kit, a disguise kit, thieves tools, two potions of cure light wounds, and a purse with 43 gp in it.
Now that combat is over and the coast appears to be clear, a wrinkled, weather-beaten halfling emerges from a hiding place. "Naleth Hundredfingers. I think you lot are friends of the scarred fellow? Think I could get an introduction?"

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Telka turns to the newly arrived halfling and smiles. Oh, we were looking for you, can you help us out with this person who just tried to murder us?
Take 10 on sense motive for 20
I am pretty sure she is a lying murderous assassin he says scowling at the woman.

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"Help out how? I don't know who she is," he replies to Telka.
Kura scowls at Telka's words and seems to clam up.

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Well, do you have any idea who she is or why she might have tried to murder us when we started asking around looking for you? Have you made any enemies lately?

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”Most people seem to have the same reaction to Torch,” Pau grumbles, nodding to the possible assassin and the halfling.

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Finally freeing herself from the alchemical ooze, Arin marches up to the captured assassin and has to restrain herself from putting an arrow through the woman's eye.
"We heard you had a message for Torch. Whether we deliver it or take you to him, either works. Do you have any idea why anyone would want to stop you from talking to him?"

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"I've seen her around. My people have some information about her, which is part of the message I wish to deliver. And as for why she would do that, to prevent the message from being delivered, of course. I would accept you passing it along for me, but would prefer to meet the man myself."

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Well, we can definitely take you to him, and we'll obviously get you there in one piece but you may want to have your people deal with her more directly. Shall we?
If everyone else is ready, we can head back to Torch with him?

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I suggest we bring her with us to see Torch, he might be interested in her.

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Dear friend, if you wish, I will do and honor you myself, punching her with pommel of falchion on back head
non lethal attack: 1d20 + 7 ⇒ (16) + 7 = 23
dmg: 2d4 + 6 ⇒ (1, 4) + 6 = 11

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Kura collapses, unconscious. An examination shows her to be stable.
The group returns to Torch with the unconscious woman and Hundredfingers in tow. The halfling explains that one of his followers found evidence that this woman was spying for the Red mantis assassins. “The Red Mantis is searching Eto for a scarred man,” he adds ominously.
When Torch hears this, he gives a noncommittal grunt and remarks that persistence does not guarantee a successful assassination.
Their business concluded, Naleth leaves. Torch thanks you for concluding that piece of business.
Elsewhere in the room, you see the rod previously retrieved, sitting on a table, cleaned and polished, with no sign of the snake corpse it was hidden in. Madam Zelekhati has also concluded her business and left. Only one task remains.
The group travels to the Caravanserai, as the time is approaching when Ionacu Lozar will be departing.
More than a dozen camels are tethered outside a large pavilion tent while a score of porters pack supplies for what looks to be a grand archeological expedition. Crates of tools, coils of rope, and sacks of dried food lie in piles waiting to divided up among the beasts of burden. Within the sumptuously appointed pavilion, stacks of scrolls and hand-drawn maps lie strewn across a canopied bed. A tall, dark haired northerner with a thick eastern accent and persistent scowl supervises the storm of activity while checking over an inventory scrawled in a well-worn ledger. “Where are those amphorae of water? This expedition won’t last a week in the Pillars of the Sun without water!”

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Pau takes the book as the group approaches the caravan, figuring he might be the most stealthy of the crew. He waits for a distraction, and plans on searching for the man’s supplies.

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Arin in pleased to see the mass of supplies laid out. Slipping a simple book among all these supplies shouldn't raise any suspicion at all.
@Pau: I'm not sure you can just grab the book. It sounds like he's actually holding it

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Reminder of the task at hand: "The academic Ionacu Lozar from the Sinomakti School of Sciences is preparing for an expedition to a site in the Pillars of the Sun. I have a scarab-marked prayer book dedicated to the god Khepri that needs to be placed among his personal effects without him suspecting anything is amiss."
Pau moves up to survey the caravan supplies. Without getting too close, he can see it will take some caution to sneak into the supplies and hide the book, as people are constantly coming and going.
We're running low on time so I'll just say the DCs flat out. A stealth check followed by a sleight of hand check will both be needed, both at a DC 20 (basically I'm assuming Lozar takes 10 on his Perception checks). People can help at these either by causing some kind of distraction (Diplomacy, Bluff, Intimidate) or by straightforward aid another.

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A DC 20 Disguise check could also be used in place of stealth (I overlooked that option earlier). If you don't trust yourself with the Stealth/Disguise and sleight of hand skills, you'll need to try a different tactic. You could try to make friends with Lozar and try to convince him that the book is a gift, or even try to sell it to him by convincing him it might be useful for his expedition. If you try either of these, a DC 15 knowledge (history or religion) check to recall something of the ancient Osirion deity Khepri would help -- otherwise you'll have to fake it with a Bluff check. Finally, he seems to be having some trouble with his suppliers -- maybe you could help him secure the supplies he needs, making your attempts to befriend him and provide a gift or sell him the book easier.

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Telka will start off by creating a distraction. Good master, do I hear you are having troibles with your supplies. Desna blesses those who are about to set out on a long journey. I woud be happy to fill any containers you have with water for your journey and grant you Desna's blessing for your undertaking.
Diplomacy: 1d20 + 6 ⇒ (7) + 6 = 13

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"Magically created water lasts only a day, don't you know that? Unless you're offering to go to the water seller and negotiate for me. Who are you, anyway?"
He notices your Desnan holy symbol, Telka, and seems a little more kindly disposed to you than he would be otherwise. The DC is 15, but worship of Desna is common in Ustalav, where Lozar comes from, and for the sake of moving ahead I'll grant a +2 circumstance bonus to your roll for that.
Pau, you basically know everything on this page.

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Do we want to offer to do some chores to help him with his supplies, or do you all want me to go straight ahead and try to talk him into the benefits of the book of Khepri, the dung beetle?

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Right now, he's not particularly friendly towards you, except insofar as you're offering to help with his supply issues. If you want to help him with his supplies, that will count as making him friendly, and then you can try to give him or sell him the book. To do that, you'll need to convince the merchants whom he has offended by refusing to haggle to forget this grievance (Diplomacy, Intimidate, or relevant Profession skill DC 15) or find other merchants to provide the goods needed instead (Appraise, Survival, or relevant Profession skill DC 15).
Otherwise, someone other than Telka would need to try for Diplomacy to make him friendly (DC 19) or at least indifferent (DC 14).
Once he's friendly, you can try to give him the book as a gift, but he isn't particularly interested in the subject, so there's two ways to do that. One is a DC 9 Diplomacy check to convince him to accept it as a favor (simple aid). The other is a Bluff check (DC 15) to convince him it may be of direct benefit for him on his expedition.
Selling him the book would require a similar Bluff check or a relevant profession check of DC 15.
Whether as a gift or a sale, getting him to accept the book will require Pau being part of the interaction, or someone else who has made the DC 15 Knowledge check as discussed in the previous post.
(If you're thinking this is kind of an excessively complicated skill challenge, I'm right there with you.)

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Given his limited capacity for public speaking, vuldruk decides to look for new providers. He was always good at finding food.
survival: 1d20 + 5 ⇒ (10) + 5 = 15

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Vuldruck finds useful suppliers easily in the market, and brings the wares to Lozar's caravan.
"Well, that's a load off my mind. So what brings you to lend aid, strangers? I'm sure you didn't just do it for the kindness of your heart, but I owe you now so I'll listen to whatever you want to try to sell me."

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Sorry but I’m out for the day. Don’t have time to put together a proper post. I’ll post tomorrow, and my plan is to tell him what I know about Khepri, an d how the book might bring him luck during his travels.

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No particular reason, we don't mind helping scholarly peoples when we can. Your lot helps the denizens of the world recover lost knowledge, after all! But now that we see where you're headed it seems fortune may have brought us here unawares. It seems we have a book which may be connected to the site you intend to visit. Given our reluctance to interfere with fate, we'd be willing to give you the book to take along. Hopefully it can help you, and if not, there is no harm. Telos smiles at him warmly.
Diplomacy, DC9: 1d20 + 4 ⇒ (9) + 4 = 13

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I know Pau needs to be involved, but here's an attempt to getting us moving on the final step.

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Yeah Let's not delay this any further, we're at the limit as it is.
Lozar takes the book and flips through it. "Khepri, hmm? What do you think of these prayers? What's your perspective on the worship of ancient gods like that instead of the ones more common in Avistan?"
Pau recalls what he knows about Khepri and gives a few details, and argues that while worship of a benevolent trickster like Khepri lacks the discipline and focus of the worship of Irori, whom he favors, it is certainly a powerful force for liberation of the downtrodden that would be agreed upon by many people in parts of Avistan and elsewhere in the world.
Lozar nods thoughtfully. "I'll keep this with me and consider its words while I travel. I'll certainly have plenty of time for reading while traveling, and while I brought plenty of books and journals with me, it can't hurt to have another. Besides, though I don't have any reason to believe that the ruins I plan to explore have a connection to Khepri, it's not beyond possibility that they could. So, I thank you."
Success! We'll wrap this up shortly.