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Here are the relevant rules that I use to allow 5 foot steps and swift actions during surprise rounds (assuming you can act in them). Bolded for emphasis.
The Surprise Round: If some but not all of the combatants are aware of their opponents, a surprise round happens before regular rounds begin. In initiative order (highest to lowest), combatants who started the battle aware of their opponents each take a standard or move action during the surprise round. You can also take free actions during the surprise round. If no one or everyone is surprised, no surprise round occurs.
Swift Actions
A swift action consumes a very small amount of time, but represents a larger expenditure of effort than a free action. You can perform one swift action per turn without affecting your ability to perform other actions. In that regard, a swift action is like a free action. You can, however, perform only one single swift action per turn, regardless of what other actions you take. You can take a swift action anytime you would normally be allowed to take a free action. Swift actions usually involve spellcasting, activating a feat, or the activation of magic items.
Take 5-Foot Step
You can move 5 feet in any round when you don't perform any other kind of movement. Taking this 5-foot step never provokes an attack of opportunity. You can't take more than one 5-foot step in a round, and you can't take a 5-foot step in the same round that you move any distance.
That being said, if you wish to sing instead, be my guest.

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ok she'll step back and cast

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Nerisiel casts as Miriel rushes forward.
Will save: 1d20 + 2 ⇒ (17) + 2 = 19
Another bolt flies out from the other eye socket and finds it mark. Hits but does not confirm due to cover. 5 damage to Nerisiel
Bolt: 1d20 + 5 ⇒ (19) + 5 = 241d8 ⇒ 5
Confirm: 1d20 + 5 ⇒ (15) + 5 = 201d8 ⇒ 8
Soon after, two other bandits scale the bridge's eastern side and rush towards you, longswords in hand.
climb: 1d20 + 4 ⇒ (17) + 4 = 21
climb: 1d20 + 4 ⇒ (20) + 4 = 24
Initiative Order
Zarina
Dwarf
Human NE
Volar
Nerisiel - 11 damage
Stephen
Miriel
Smiler
Human NW
Human N
Human S
Maranax
Zarina is up!

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Volar moves up and draws his weapon while making sure Smiler stays with him. Move and draw weapon. No BAB so can't combine them just yet.

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Doublechecked the range increment on the crossbow, the first shot would have missed you Nerisiel. You are only hit by the second one. So only 5 damage total.

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"Zarina I think it's time for our duet. Here's my staring note OWowowow" she looks at the one bolt and is thankfull it is not two like her brief double vision suggested

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The dwarven bandit-woman screams "Hurry, you dolts, I can't do this all by myself!" and drives her dagger into a soft spot in the still startled Nerisiel.
stab vs Nerisiel: 1d20 + 4 ⇒ (18) + 4 = 221d4 + 2 ⇒ (2) + 2 = 4
sneak attack: 1d6 ⇒ 5
A bolt flies past Miriel.
bolt vs miriel: 1d20 + 3 ⇒ (9) + 3 = 121d8 ⇒ 4
Initiative Order
Volar
Nerisiel - 14 damage
Stephen
Miriel
Smiler
Human NW
Human N
Human S
Maranax
Zarina
Dwarf
Human NE
Volar, Nerisiel (finally), Stephen, Miriel, Smiler are all up!

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"Shelyn, melme ar Ainulindalë!" Miriel calls the power of her goddess as she closes on the dwarf. "Your tale ends now!" she shouts at the dwarf, slicing down with all her might.
Smite power attack: 1d20 + 7 + 1 ⇒ (16) + 7 + 1 = 24
Damage: 1d10 + 9 + 1 ⇒ (10) + 9 + 1 = 20
Smite evil. Reduce hit by 2 and damage by 3 if not evil.

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Volar says a few words of magic as he reaches over to touch Smiler's shoulder. A brief glow of verdant green energy flows up and around the ape's jaw, then quickly fades to a less noticeable earthy brown. Magic Fang on bite attack.
Once his spell is complete Volar gives a whistle for Smiler to attack and points towards the woman.
Volar stays back for now and waits to move forward until he's needed.

Smiler |

Smiler does as his friend commands and moves in cautiously then tries to bite the woman. I'll let you move him GM unless you prefer me to do so.
bite attack, magic fang: 1d20 + 2 + 1 ⇒ (12) + 2 + 1 = 15
bite damage, magic fang: 1d4 + 1 + 1 ⇒ (1) + 1 + 1 = 3

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Volar, yes you give the orders and I'll move him. Feel free to continue to roll his regular attacks.
Nerisiel steps back and with a flick of her wrist sends the dwarf's dagger flying. Others move forward to fight (or send others forward).
Miriel engages the dwarf with a powerful call to Shelyn, who most definitely is listening in on this windy pass. With a righteous fury Miriel splits hard into the dwarf's shoulder, and she follows the arc of the sword to the ground, unconcious, just before Smiler arrives.
Smiler grunts and continues his assault toward the other bandits, galloping on thick arms and legs.
Another bolt flies from the stone dwarf's visage.
bolt vs Nerisiel: 1d20 + 3 ⇒ (7) + 3 = 101d8 ⇒ 8
"Aye, don't shoot at that one. Shoot at the one that dropped Fowrah with one blow."
"No, you heard her, kill them one at a time."
The two other bandits hesitantly circle the ape and then attack viciously. 12 damage to Smiler
Smiler's AOO: 1d20 + 3 ⇒ (13) + 3 = 161d4 + 2 ⇒ (4) + 2 = 6
Stab vs Smiler: 1d20 + 7 ⇒ (7) + 7 = 141d8 + 3 ⇒ (1) + 3 = 4
Stab vs Smiler: 1d20 + 7 ⇒ (20) + 7 = 271d8 + 3 ⇒ (5) + 3 = 8
Confirm vs Smiler: 1d20 + 7 ⇒ (6) + 7 = 131d8 + 3 ⇒ (7) + 3 = 10
Initiative Order
Maranax
Zarina
Dwarf - out of combat
Human NE
Volar
Nerisiel - 14 damage
Stephen
Miriel
Smiler - 12 damage, out of combat
Human NW
Human W
Human E
Maranax and Zarina are up!

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Seeing no immediate threat to himself, Maranax cocks, loads and fires his light crossbow, aiming for one of the enemy figures on the bridge but aiming too high and sending the bolt flying off into the ravine.
Light crossbow: 1d20 + 2 ⇒ (2) + 2 = 41d8 ⇒ 2

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Another bolt flies harmlessly past.
bolt vs Nerisiel: 1d20 + 3 ⇒ (5) + 3 = 81d8 ⇒ 2

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Initiative Order
Volar
Nerisiel - 14 damage
Stephen
Miriel
Smiler - 12 damage, out of combat
Human NW
Human W
Human E
Maranax
Zarina
Dwarf - out of combat
Human NE
Volar, Nerisiel, Stephen, Miriel are up!

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"Hey backup dancers, your lead is down, so give up or die!" Miriel shouts at the bandits, charging the closest one on the last word.
Attack (power attack, charge): 1d20 + 5 + 2 + 1 ⇒ (12) + 5 + 2 + 1 = 20
Damage: 1d10 + 6 + 1 ⇒ (6) + 6 + 1 = 13
Moved on map next to target. AC now 17 (charge)

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Nerisiel moves up trying to find some cover behind Miriel and casts hideous laughter on one of the ape killers (will save dc13)
"Hail the mighty monkey maulers"

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Volar moves up as fast as he can to try to heal his friend.
"You're going to pay for hurting my friend you bandit scum!" he shouts as he rushes forwards.

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The bandit braces his mind as Nerisiel casts her spell. He is not as successful as Miriel's attack finds his weak spot. He takes a step back pulls a potion and drinks it.
will save: 1d20 + 3 ⇒ (20) + 3 = 23
potion: 1d8 + 1 ⇒ (4) + 1 = 5
Another bolt flies from the dwarf-face.
bolt: 1d20 + 5 ⇒ (18) + 5 = 231d8 ⇒ 2
2 points damage to Miriel
The final bandit charges Miriel as well.
bolt: 1d20 + 7 ⇒ (15) + 7 = 221d8 + 3 ⇒ (6) + 3 = 9
9 more points damage to Miriel
Initiative Order
Stephen
Maranax
Zarina
Dwarf - out of combat
Human NE
Volar
Nerisiel - 14 damage
Miriel - 11 damage
Smiler - 12 damage, out of combat
Human NW - In Dwarf-Face
Human N - 8 damage
Human S
Stephen, Maranax and Zarina are up!

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Stephen casts his spell as he approaches, the bandit braces himself and holds his balance. Zarina takes advantage of his concentration and hits him with her arrow square in the chest. Another bolt flies from the mountain face and strikes Volar weakly. 1 point of damage to Volar
reflex for grease: 1d20 + 1 ⇒ (17) + 1 = 18
bolt at Volar: 1d20 + 5 ⇒ (17) + 5 = 221d8 ⇒ 1
self-stabilize for Smiler DC 13: 1d20 + 0 ⇒ (16) + 0 = 16 success
Initiative Order
Maranax
Volar - 1 damage
Nerisiel - 14 damage
Miriel - 11 damage
Smiler - 12 damage, out of combat
Human (orange)
Human (green) - 8 damage
Human (blue) - 3 damage
Stephen
Zarina
Dwarf - out of combat
Human (yellow)
Maranax, Volar, Nerisiel and Miriel are up!

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Volar steps over to Smiler and places his hands on the ape as he chants some words of divine healing.
Cure Light Wounds: 1d8 + 1 ⇒ (8) + 1 = 9
"Come on my friend, we have more adventures to go on!"

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Nerisiel attempts to trip the bandit
trip attack with whip: 1d20 + 7 ⇒ (1) + 7 = 8
"You will fall"
She drops the whip and curses in elven

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"Varyavanië", Miriel says a swift prayer and touches her wounds, which close under the divine power.
Lay on hands: 1d6 ⇒ 3
"Do your part as she said and die! Die!" Miriel shouts at the bandit, swinging her blade wildly.
Attack (power attack): 1d20 + 5 + 1 ⇒ (16) + 5 + 1 = 22
Damage: 1d10 + 6 + 1 ⇒ (5) + 6 + 1 = 12
If the bandit drops, move next to the other bandit, avoiding the grease.

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The bandit squeals as Maranax pelts him with an arcane missile. Volar carefully slides over to his ape through the grease, avoiding the bandit's wild swing, and heals him. Nerisiel's whip misses its mark completely but Miriel strikes true once again. As his companion falls and Miriel advances on him, the other bandit (green) drops his weapon with a clatter on stone and raises his arms.
"No more, please, this wasn't my idea." He says with squinted eyes.
There is a brief pause before another bolt rips the air from the eye-socket, barely missing Miriel, or perhaps the bandit. "You coward!" calls from within the dwarf-face.
acrobatics for Volar to move into grease.: 1d20 - 1 ⇒ (18) - 1 = 17
AOO on Volar: 1d20 + 5 ⇒ (5) + 5 = 101d8 + 3 ⇒ (5) + 3 = 8
bolt vs Miriel: 1d20 + 5 ⇒ (15) + 5 = 201d8 ⇒ 3
Initiative Order
Smiler - 3 damage, prone
Stephen
Zarina
Dwarf - out of combat
Human (yellow)
Maranax
Volar - 1 damage
Nerisiel - 14 damage
Miriel - 8 damage
Human (orange)
Human (green) - 8 damage, surrendered
Human (blue) - 20 damage, out of combat
Smiler can take action again. Stephen and Zarina are also up!

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Does inspired courage increase magic missile damage?
Zarina continues to inspire the troops. As she does so, she moves into the fray, using her whip to provide Miriel aid with her target.
Aid vs AC 10: 1d20 + 5 ⇒ (16) + 5 = 21
Gives Miriel +2 to hit her target or +2 AC for round

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Inspire Courage only affects weapon damage, not spells (except, rays and others per this FAQ).
Zarina and Stephen maneuver into position to help. The bolts keep on flying (and missing), Miriel the target still.
bolt: 1d20 + 5 ⇒ (6) + 5 = 111d8 ⇒ 3
Initiative Order
Smiler - 3 damage, prone
Maranax
Volar - 1 damage
Nerisiel - 14 damage
Miriel - 8 damage
Human (orange)
Human (green) - 8 damage, surrendered
Human (blue) - 20 damage, out of combat
Stephen
Zarina
Dwarf - out of combat
Human (yellow)
Smiler, Maranax, Volar, Nerisiel, and Miriel are up! Note that the only two left fighting you are the bandits firing bolts from the mountainside.

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Miriel raises her blade at the bandit, but stops when she hears the surrender. "Beautiful", she snarls through gritted teeth, and snaps her attention toward the hidden enemies. She rushes toward the stone dwarf face, cursing at the bandits: "I'll rip you out of that face, and paint it with your blood!" She finishes with another call to her goddess: "Varyavanië!", and her wounds again close under her touch.
Lay on hands: 1d6 ⇒ 2
What does Miriel actually see? The enemies are behind stone, is it possible to attack them from outside, with melee or reach? Is there a way around clearly visible?

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They are quite visible, the eye sockets are so large as to provide them no cover. It is about 15 feet up to their location, however.

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Are they higher than ground level? Is it possible to charge on the nose and hit them from there?
Edit: Do you mean they are 15ft from the ground so have to climb? I first read the '15 feet' as 'you are still 15ft away' but then on second reading maybe understood correctly.

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Nerisiel searches the dwarfs body for potion bottles. "If there are still arrows flying when I find the healing potion I'll be drinking it for myself"
perception: 1d20 + 7 ⇒ (18) + 7 = 25

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Sorry, it was not clear. They are 15 feet above ground level, so climbing (or ranged attacks) will be necessary.

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Volar points at the man firing at them all and whistles to attack him. He then grabs his healing wand and says to the group "If anyone is hurt please let me know."

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Smiler shakes his head and regains his footing, and awaits Volar's command. Maranax blasts one of the remaining holdouts with his force missile, while Miriel heals again and approaches with a fearsome curse, dodging another bolt aimed at her from above.
With a sharp whistle Volar sends Smiler to the cliff-face and turns his eyes to the party. Nerisiel quickly searches the dwarf woman and finds not one but two vials. One contains a oily metallic substance and the other a thin bluish liquid.
handle animal DC12: 1d20 + 10 ⇒ (12) + 10 = 22
bolt: 1d20 + 6 ⇒ (9) + 6 = 151d8 + 1 ⇒ (4) + 1 = 5
GM stuff: 20d20 ⇒ (8, 7, 12, 10, 8, 12, 14, 17, 13, 18, 18, 7, 4, 6, 17, 11, 8, 8, 5, 12) = 215
Initiative Order
Stephen
Zarina
Dwarf - 20 damage, out of combat
Human (yellow)
Maranax
Volar - 1 damage
Smiler - 3 damage
Nerisiel - 14 damage
Miriel - 6 damage
Human (orange)
Human (green) - 8 damage, surrendered
Human (blue) - 20 damage, out of combat
Stephen and Zarina are up!

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I forgot the force missile damage, so ... Human (orange)- 3 damage

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reflex: 1d20 + 3 ⇒ (8) + 3 = 11
bolt: 1d20 + 5 ⇒ (15) + 5 = 20

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The man in the eye realizes the spell is coming and braces his feet. He fires a bolt at Stephen in retaliation, but misses.
reflex: 1d20 + 3 ⇒ (20) + 3 = 23
bolt: 1d20 + 5 ⇒ (5) + 5 = 10
Initiative Order
Zarina
Maranax
Volar - 1 damage
Smiler - 3 damage
Nerisiel - 14 damage
Miriel - 6 damage
Human (orange) - 3 damage
Human (green) - 8 damage, surrendered
Human (blue) - 20 damage, out of combat
Stephen
Dwarf - 20 damage, out of combat
Human (yellow)
Everyone except Stephen is up!

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"You worthless critic, calling someone coward while hiding!" Miriel shouts, spitting out the 'critic' as if it was a vulgar word. She tries to get up to the eyes with the momentum from her dash.
climb: 1d20 + 2 - 4 ⇒ (16) + 2 - 4 = 14
Yes, untrained and armor check penalty.