She cogitated deeply on the problem before coming up with a solution.
about
Frequency:
60
%
He cogitated about the implications of his decision.
on
Frequency:
50
%
The team cogitated on the best strategy to win the game.
over
Frequency:
45
%
She cogitated over the details of the contract before signing it.
Idiomatic Expressions for cogitate
Phrase: put one's brain in gear
Meaning: to start thinking seriously and carefully about something
Usage: Before giving an answer, he needs to put his brain in gear and cogitate on the question.