In a manner that shows careful planning and caution; with deliberate wariness.
From cautelous + -ly adverbial suffix. The -ly ending converts the adjective into an adverb indicating the manner in which something is done.
Adverbs like this one are disappearing from English—it's so much easier to say 'cautiously' that 'cautelously' sounds almost Shakespearean now. Language naturally selects the shorter, easier version.
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