Work diligently: you work hard all day, get a +4 on a single roll for your days duties.
Influence: you take your rolls as normal, and get an opportunity to influence one of the people on the boat.
Sneak: you do your job as usual, but take one brief opportunity to sneak off and explore. You can take a single perception check about part of the ship, or any other single check if you want.
Shop: take a -2 on all your checks, as you got to visit the quarter master store.
Shirk: -2 on all your checks, explore the ship more broadly and take a 10 on perception, but you also have to make a check to avoid detection.
Nighttime Ship Actions
Sleep: Go to bed early and sleep through the night (automatically recover from fatigue)
Gamble: Play or gamble on a game of chance or pirate entertainment
Entertain: Make one Perform check to entertain the crew.
Harrow: I'll let you make a Harrow reading for yourself, or for shipmate here. It's a Profession (Fortune-Teller Check) for others, but for yourself you get an additional +4 modifier.
Influence*: Attempt to influence a single NPC
Sneak*: Take time exploring one area of the ship. The PC can take 20 on a single Perception check or other skill check, but must make a check to avoid being discovered.
Steal*: Attempt to open a locked door or locker. The PC must make a check to avoid being discovered.
Additionally, you can attempt to take up to two additional ship actions during the middle watch in the dead of night (any nighttime ship action marked with an asterisk), but to do so the PC must make a successful constitution check (DC 10, +4 per extra ship action taken) or be fatigued for the next day.