The use of adverbs in english

I just realized that I need to get help with understanding how to use adverbs in English. Let's say that a guy is nice, and he performs every action in that way.

Does he:
a) act nice
b) act nicely

Which one is the correct one and why is it so? Don't be afraid to use grammatical terms.

"Nicely" is only an adverb while "nice" is only an adjective. "He acts nice" or similar examples are idiomatic phrases and are grammatically incorrect regardless of the shades of connotation brought up by >>2

"With niceness (noun) in mind, he nicely (adverb) conducts nice (adjective)acts"