The number of actions per turn per faction in Skyward Collapse seems to be inconsistent and I haven't been able to figure out what determines the number of actions available to the factions across the turns.
You begin the game with nine actions. At any point in time you can have up to 9 actions in your pool. Each turn, each faction is granted 3 actions; if you do not use them all, the unused actions are banked for use in later turns. Actions over the cap of 9 are lost.
This might vary with difficulty but I doubt it.