In a clever, shrewd, or cunning manner; with careful judgment and subtle intelligence.
From astucious + -ly (adverb suffix). The adverbial form of the adjective astucious, following standard English adverb formation patterns.
Adverbs ending in -ly can sometimes sound awkward when the adjective already implies manner (like 'astuciously' from 'astucious'), which is why 'astutely' has become the preferred modern form for the same meaning.
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