excogitate vs bethink

excogitate and bethink both are verbs.

Word	Noun	Adjective	Verb	Adverb
excogitate	No	No	Yes	No
bethink	No	No	Yes	No

As verbs, bethink is a hyponym of excogitate; that is, bethink is a word with a more specific, narrower meaning than excogitate:

Other hyponyms of excogitate include premeditate, theologise, theologize, introspect, cogitate, question, wonder, puzzle, consider, study.

excogitate (verb)	bethink (verb)
reflect deeply on a subject	consider or ponder something carefully
come up with (an idea, plan, explanation, theory, or principle) after a mental effort	cause oneself to consider something