analyze vs work through

analyze

verb
  • To examine in such a manner as to ascertain the elements or nature of the thing examined; as, to analyze a fossil substance, to analyze a sentence or a word, or to analyze an action to ascertain its morality. 

  • To subject to analysis. 

  • To separate into the constituent parts, for the purpose of an examination of each separately. 

  • To resolve (anything complex) into its elements. 

work through

verb
  • Used other than figuratively or idiomatically: see work, through. 

  • To get past a difficult or stressful situation by thinking or talking about it. 

How often have the words analyze and work through occurred in a corpus of books? (source: Google Ngram Viewer )