"deeply think" is a correct and usable phrase in written English.
It means to think deeply or intensely about something. You can use it in any sentence where you want to convey a strong level of contemplation or introspection. Example: After experiencing a life-changing event, she sat alone in her room and deeply thought about the direction of her life.
"I like to hope for the best in people, but I deeply think the Republicans are not going to be any help and they're going to block everything, even if the end result would be better for the country," said Amanda White, 24.
When you deeply think about it, disruption is a pretty unpleasant word to be associated with.
The 'Eclipse' position, where the hood can be turned around to cover your face completely, is for when you need to truly switch off from your surroundings, such as to deeply think, take a short break or meditate.
Everyone is so passionate about the piece, about each other, and about spreading the messages we deeply think are important.
The cold weather justifies the desire to stay in by a fireplace or space heater and just work on the self, a time to deeply think about things and turn physical inactivity into internal mental action.
Once behind cover or concealment, breathe deeply, think "I will live," and assess the situation.
Spontaneous, informal, deeply thought, and deeply felt, these are among the best letters written by any English poet.
Nemorino, a young man who feels deeply, thinks himself a nobody.
His theatre directing is always visually attractive, deeply thought through, stripped down and provocative.
Bernardin lit a cigarette as he contemplated confronting the restaurant's management, but, after inhaling deeply, thought better of it.
What Mr Sullivan has to say about those subjects; indeed, what he has to say about most things is interesting, elegantly expressed and deeply thought through.
