set out vs undertake

set out

verb
  • To start an activity with the intention of finishing it. 

  • To explain something, or give exact details, usually in writing. 

  • To go out, leave. 

  • To position, to put in a position 

undertake

verb
  • To take upon oneself; to start, to embark on (a specific task etc.). 

  • To commit oneself (to an obligation, activity etc.). 

  • To pass a slower moving vehicle on the curbside rather than on the side closest to oncoming traffic. 

noun
  • The passing of slower traffic on the curbside rather than on the side closest to oncoming traffic. 

How often have the words set out and undertake occurred in a corpus of books? (source: Google Ngram Viewer )