In a manner that involves thinking, meditating, or pondering; thoughtfully.
Derived from cogitant plus the adverbial suffix -ly, creating an adverb from the noun form. This follows the standard English pattern of turning nouns of agency into adverbs.
It's rare and somewhat archaic, but when you use it, you're describing the way someone thinks deeply—it's the adverbial cousin of 'cogitate' that almost nobody remembers.
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