adverb
An adverb is a word that modifies a verb, adjective, or another adverb. It often indicates manner, time, place, or degree. In this case, 'closely' modifies how something is done or performed.
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The scientists closely monitored the experiment to ensure accurate results.
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I watched the movie closely because I didn't want to miss any details.
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I was creeping on his social media profile closely to see if he was dating someone new.
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She listened closely to his words, trying to decipher the hidden meaning behind them.