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Improvise (verb)
To make something up or invent it as one goes on; to proceed guided only by imagination, instinct, and guesswork rather than by a careful plan.
“He had no speech prepared, so he improvised.”
“They improvised a simple shelter with branches and the rope they were carrying.”
“She improvised a lovely solo.”
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Improvize (verb)
alternative spelling of improvise
Wiktionary