Last thing before you go to bed, get stuck on a problem. Go to bed. You'll wake up with a solution, and in the meantime get to lay in a comfy bed for hours, and maybe even have some cool dreams. Best brain hack ever.
For me, that usually just leads to insomnia. If I read anything remotely interesting within an hour or so of bed, it takes me a long time to wind down. YMMV.
When I'm stuck during the day, a context change (such as a gym break) often has the same effect though.
Why waste it? It's a perfectly valid state of consciousness. Look into dreaming techniques such as lucid dreaming. You might find creative solutions to problems or new ideas to integrate into your waking life.