muse

nouns

the source of an artist's inspiration
"Euterpe was his muse"
is a type of (narrower)
anything that provides inspiration for later work

verbs

reflect deeply on a subject
"I mulled over the events of the afternoon"; "philosophers have speculated on the question of God for thousands of years"; "The scientist must stop to observe and start to excogitate"
is derived from
is derived from