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Can we say we copy someone in terms of his or her behaviour?

For example, a child copied someone's mischievous behaviour.

Is "imitate" a better word?

What is the best word for such meaning?

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"Copy" is a great word for that. We even call a person who imitates another person a "copycat." It is very common and correct. "Imitate" and "mimic" are also good.