Is an action a verb or an adjective?

Answer 1

It could be both.

Strictly speaking, a word that denotes an action is a verb, e.g.:

The Earth shook.

Here, 'shook' is the past tense form of the verb 'to shake', which is an action.

An adjective is a word that describes another, e.g.:

The shaking boy wasn't sure whether the present participle of the verb 'to shake' in this sentence is an adjective or not.

Here, 'shaking' is describing the boy. Shaking is still an action and therefore a verb, but it's also a description, and therefore an adjective. We call such words 'adverbs'.

Have fun...