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To devise; to develop or invent something from one's thoughts. A noun or pronoun can be used between "think" and "up." I'm sure our R&D department will be able to think up a solution to the issue. He thought the story up while he was sailing along the coast of Spain.
think something up
to contrive or invent something. Don't worry. I'll find a way to do it. I can think something up in time to get it done. John thought up a way to solve our problem.
Devise, contrive by thinking, as in She's an expert at thinking up interesting programs. [Mid-1800s]
To devise or develop something: She thought up a plan to make more money. He thought the design up all by himself.