contrive

(verb) make or work out a plan for; devise. Synonyms: plan, project, design. Examples: "They contrived to murder their boss." "Design a new sales strategy." "Plan an attack."

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

(verb) put or send forth. Synonyms: project, cast, throw. Examples: "She threw the flashlight beam into the corner." "The setting sun threw long shadows." "Cast a spell." "Cast a warm light."