act on vs influence

act on

verb
  • To affect something. 

  • To act decisively on the basis of information received or deduced. 

  • Το act accordingly to a (usually sublimated) desire or impulse. 

  • To take action against something. 

influence

verb
  • To have an effect on by using gentle or subtle action; to exert an influence upon; to modify, bias, or sway; to persuade or induce. 

  • To exert, make use of one's influence. 

noun
  • A person or thing exerting such power or action. 

  • Electrostatic induction. 

  • The power to affect, control or manipulate something or someone; the ability to change the development of fluctuating things such as conduct, thoughts or decisions. 

  • An element believed to determine someone's character or individual tendencies, caused by the position of the stars and planets at the time of one's birth. 

  • An action exerted by a person or thing with such power on another to cause change. 

How often have the words act on and influence occurred in a corpus of books? (source: Google Ngram Viewer )