Since no one has yet posted an action, I'm guessing there is some uncertainty about it.
First of all, you can pretty much do anything you wish. You can't magically create resources, but that's the only hard limitation. So no creating an army to besiege Laria, although you can use your current troops in your action.
The more you're attempting to gain, the harder it will be to gain it. For example, if your PC decides to marry into a landed family and acquire land as a dowry (in effect gaining the Village asset) it will be more difficult than taking your troops to patrol a merchant caravan for some easy renown / a small payment. The more open-ended actions are more likely to have a range of success, rather than the more firm succeed/fail actions. That example is intriguing in the court of one of the non-Supporters in an attempt to gain influence there. A great success might earn your Order a Chapterhouse in that city and empower the Order, while a lesser success might simply earn some influence with NPCs should an event occur there.
Traits will have some impact, so Silver Tongued characters will have an easier time with actions that involve persuasion rather than simple combat alternatives like escorting caravans.
Since we've never done this before, it's of course a work in progress.