Ellos se mantuvieron firmes a sus convicciones.

firmes, in this sentence, is not a verb form, even though it is a homonym with one, so it does not belong in this grammar exercise.

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But I think here, ‘firmes,’ describes how they maintain their convictions: firmly. I’m thinking it’s an adjective, and not a verb?

Here it’s an adverb:

a word or phrase that modifies or qualifies an adjective, verb, or other adverb or a word group, expressing a relation of place, time, circumstance, manner, cause, degree, etc. (e.g., gently, quite, then, there).

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That’s right! Thanks!