contemplate (v): to think deeply or carefully about (something)
Definition from Merriam-Webster (http://www.merriam-webster.com/dictionary/contemplate)
From What You Pawn I Will Redeem by Sherman Alexie (In the part of 6a.m)
He thought about that for a while. He contemplated it. I liked that about him.
When Jackson asked Officer Williams if it is scary being a cop, Officer Williams thought deeply and carefully about that question.