WordNet (r) 3.0 (2006):

act on
    v 1: carry further or advance; "Can you act on this matter
         soon?" [syn: pursue, follow up on, act on]
    2: regulate one's behavior in accordance with certain
       information, ideas, or advice; "The Founding Fathers acted on
       certain moral principles"

Moby Thesaurus II by Grady Ward, 1.0:

54 Moby Thesaurus words for "act on":
   act upon, affect, approach, bear a hand, bear upon, concentrate on,
   condemn, decree, do something, do something about, doom, draw,
   draw on, exert influence, find, find against, find for, focus on,
   get cozy with, get with it, go, influence, lead on, lift a finger,
   lobby, lobby through, magnetize, make advances, make overtures,
   make up to, maneuver, operate on, order, pass judgment,
   pass sentence, proceed, proceed with, pronounce,
   pronounce judgment, pronounce on, pull strings, report,
   return a verdict, rule, sentence, strike a blow, take a hand,
   take action, take measures, take steps, treat, utter a judgment,
   wire-pull, work on