What is the adverb think?

The participial form of "to think" is "thought" so the adjectives would include thoughtful or thoughtless, and the adverbs thoughtfully and thoughtlessly. The present participle (thinking) creates the adverb unthinkingly. The adjective unthinkable creates the adverb unthinkably.

Thoughtfully is the adverb form derived from think.

Adverbs that can be used with the verb think are:

clearly

cleverly

creatively

resourcefully

passionately

objectively

impartially

fairly