excogitate

(verb) come up with (an idea, plan, explanation, theory, or principle) after a mental effort. Synonyms: invent, contrive, devise, formulate, forge. Example: "Excogitate a way to measure the speed of light."

(verb) reflect deeply on a subject. Synonyms: chew over, think over, meditate, ponder, contemplate, muse, reflect, mull, mull over, ruminate, speculate. Examples: "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."