In a manner that involves gazing or looking steadily at something.
From 'gaze' (to look steadily), plus the adverbial suffix '-ly' which converts adjectives and verbs into adverbs describing how something is done.
This word is rarely used in modern English, but it's a perfect example of how English lets us turn almost any verb into an adverb—though we'd usually just say 'while gazing' instead!
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