OED mentions that the sense "to make, do, perform (an act, action, movement, etc.); to carry out." of the verb take is a periphrastic usage and the earliest citation for this sense is from c1380:
Often take forms with the object a phrase which is a periphrastic equivalent of the cognate verb: e.g. to take a leap is equivalent to to leap, to take a look to to look, to take one's departure to to depart, etc.
Oxford English Dictionary, s.v. “take, v., sense IX.83.a”, July 2023. https://doi.org/10.1093/OED/8480914419
And for the etymology, OED says that the French verb prendre may have influenced the development of additional senses of the verb take:
French prendre to take (see prend v.) is attested in a similar range of senses, some of which appear to have influenced the semantic development of the English verb.
take v. also occurs in a large number of idiomatic phrases which correspond to (and in many cases are influenced by) parallel constructions in French with prendre. For further discussion see L. Iglesias-Rábade in D. A. Trotter Multilingualism in Later Medieval Brit. (2000) 93–130.
Oxford English Dictionary, s.v. “take, v., Etymology”, July 2023. https://doi.org/10.1093/OED/4265677235
Note: Prend is an obsolete, rare verb in English meaning "To take; (also) to understand, comprehend." from 1447, per OED.
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