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.

>>3
grammatically incorrect regardless of the shades of connotation brought up by >>2
>>4
There's not much of a difference to me...

Well yeah, colloquial English tends to be grammatically incorrect if you hold a prescriptivist view like >>3 does, but to me it is normal, if dialectal speech. Dropping the -ly ending while still using the word as an adverb is a pretty salient feature of spoken [American] English.

To sum up: act nicely = standard English, act nice = colloquial English.