Step 1 (Recall definitions).
An adverb modifies a verb, adjective, or another adverb — it tells how, when, where, or to what extent an action is done.
An adjective modifies a noun or pronoun — it describes a quality or attribute.
Step 2 (Find the adver(b).
The main verb in the sentence is "climbed". The word "quickly" describes how} the cat climbed. Therefore, "quickly" is the adverb.
Step 3 (Find the adjective).
The noun "tree" is being described as "tall". Therefore, "tall" is the adjective.
Step 4 (Conclusion).
Adverb = quickly, Adjective = tall.
\[
{\text{Adverb: quickly; Adjective: tall (Option (a)}}
\]