Participle is the correct answer.
Explanation:
A participle is a word formed by a verb and used as noun or as an adjective; they are also used to make compound verb forms. In this case, the participle is formed with the verb + ing as in planning.
An infinitive is the basic form of a verb. It can be identified because it uses "to" before the verb.
A verb phrase contains a main verb or a main verb plus a modal auxiliary or any other auxiliary.