Set about; pledge (9)
I believe the answer is:
undertake
I believe this is a double definition.
'set about' is the first definition.
(synonyms)
'pledge' is the second definition.
(thesaurus)
(Other definitions for undertake that I've seen before include "Guarantee" , "drive dangerously?" , "Promise - perform" , "Accept - promise" , "Agree or promise to do something" .)