Marc P. answered 12/29/19
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It looks like you answered your own question! I'd just add that "verb tenses" are not a part of speech. Tense is a property of verbs, and a finite verb is conjugated based on its tense. For example, for the present tense you might conjugate the verb "to walk" as "walks," but for the past tense you would conjugate the same verb as "walked." In either case, the part of speech is simply "verb."