CEREBRATE
think, cogitate, cerebrate
(verb) use or exercise the mind or one’s power of reason in order to make inferences, decisions, or arrive at a solution or judgments; “I’ve been thinking all day and getting nowhere”
Source: WordNet® 3.1
Etymology
Verb
cerebrate (third-person singular simple present cerebrates, present participle cerebrating, simple past and past participle cerebrated)
To think or cogitate, especially so as to make inferences or decisions or to solve problems.
Source: Wiktionary
Cer"e*brate, v. i. (Physiol.)
Definition: To exhibit mental activity; to have the brain in action.
Source: Webster’s Unabridged Dictionary 1913 Edition