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By writing things down, you empty your mind of unnecessary information and rely on your notes and writing for storage of knowledge and information. Then, your attention and decision making ability (which is finite and takes time to restore) can be more efficiently applied to actually generating valuable thoughts and ideas.
Rather than mentally choosing what information to remember, mentally choosing what to do next, mentally choosing what you will have to do, write things down to save your mental energy. Writing it down also gives you a good idea of how much stuff you will have to do every day, how long you will have to spend on it, and when or where you should complete it, which you can then plan with minimal workload for your mind.
Your brain will thank you for exhausting it less quickly.
See other reasons for why I write everything down.