In a calm, composed manner without panic or emotional reaction; while maintaining a cool head.
From 'coolheaded' (adjective) plus the adverbial suffix '-ly.' This standardized adverb form emerged in formal English writing in the 19th century.
Adverbs ending in '-ly' are less common in modern speech than written English—people say 'cool-headed' more often than 'coolheadedly,' showing how informal English drops these formal adverbial forms.
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