come up with (an idea, plan, explanation, theory, or priciple) after a mental effort; "excogitate a way to measure the speed of light"
If you formulate a thought, opinion, or idea, you express it or describe it using particular words. I was impressed by the way he could formulate his ideas. = articulate
To reduce to, or express in, a formula; to put in a clear and definite form of statement or expression
put into words or an expression; "He formulated his concerns to the board of trustees"
If you formulate something such as a plan or proposal, you invent it, thinking about the details carefully. Little by little, he formulated his plan for escape. = devise