cogitate

verbs

consider carefully and deeply; reflect upon; turn over in one's mind
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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"
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"
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