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most cautiously
more cautiously, most cautiously
The word "cautiously" is an adverb. It modifies a verb (e.g., walk cautiously) or another adverb or adjective (e.g., speak very cautiously).
I entered the unlit room cautiously.
The boy cautiously tested the water.
The two adverbs are "somewhat" and "cautiously."
Cautiously modifies entered and somewhat modifies cautiously.