You can make ~하게 when a verb is like be.
Such as, v친절하다(be kind) → a친절하게(kindly)
However, if a verb is like think and make, you can't make it.
v생각하다(think) → 생각하게 X (thinkly? no)
A adverb is from a adjective.
친절한 → 친절하게
당당한 → 당당하게
but 생각한? → 생각하게? (x)
However, you can use 생각하게, if you want other person to think something.
생각하게 ( tone of command, polite )
Also, ~생각하게 and 공부하게 etc are used as a abbreviation of ~하기 위해(for ~ing)