make or work out a plan for; devise; "They contrived to murder their boss"; "design a new sales strategy"; "plan an attack"
come up with (an idea, plan, explanation, theory, or principle) after a mental effort; "excogitate a way to measure the speed of light"
put or send forth; "She threw the flashlight beam into the corner"; "The setting sun threw long shadows"; "cast a spell"; "cast a warm light"