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EXCOGITATE

Definition:

[verb] come up with (an idea, plan, explanation, theory, or priciple) after a mental effort; "excogitate a way to measure the speed of light"
Synonyms: invent, contrive, devise, formulate, forge
[verb] reflect deeply on a subject; "I mulled over the events of the afternoon"; "philosophers have speculated on the question of God for thousands of years"; "The scientist must stop to observe and start to excogitate"
Synonyms: chew over, think over, meditate, ponder, contemplate, muse, reflect, mull, mull over, ruminate, speculate