1. cogitate -- (consider carefully and deeply; reflect upon; turn over in one's mind)
2. think, cogitate, cerebrate -- (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")
1.
That evening Tommy sat on the bed, and cogitated deeply. - from The Secret Adversary by Agatha Christie