Answer:
My hunch is that the adverb "mente" is used to modify adjectives and indicates the manner or way in which something is done. It is added to the feminine singular form of the adjective. For example, the adjective "rápido" (fast) becomes "rápidamente" (quickly). I also suspect that this pattern follows the general rule that adverbs usually come after the verb they modify in Spanish.
After reviewing the examples, I think my hunch is correct. The adverb "mente" is added to the feminine singular form of the adjective, and it modifies the adjective to indicate the way or manner in which the action is done. Additionally, the adverb usually comes after the verb it modifies. For example, "Habló claramente" (He spoke clearly) and "Caminamos lentamente" (We walked slowly).