The answer is very
An adverb modifies a verb, an adjective, a clause, another adverb, or a phrase. In simpler terms, it can describe how, where, when, at what intensity, what frequency or to what extent an action takes place.
"Very" is ad adverb of dregree (it indicates us the intensity of something). In the sentence, it tells us about the intensity of another adverb "carefully". Other examples of adverbs of degree are "too", "extremely", "enough", "quite", "rather", "fully" and "just".
