"Entropy" and "action" are two entirely different concepts. The first relates to coarse-grained statistical description of a physical system at macroscopic scales, the latter to the underlying deterministic microscopic dynamics exhibited by the system.
Think about pool billard: the balls collide according to Newtons laws which can be expressed by stating that the balls trajectories minimize a quantity called 'action'. At the same time we could make a statistical statement that during the game the mean distance between the balls doesn't decrease.