Verb
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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"
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come up with (an idea, plan, explanation, theory, or principle) after a mental effort
"excogitate a way to measure the speed of light"
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make or work out a plan for
devise
"They contrived to murder their boss"
"design a new sales strategy"
"plan an attack"