how do you cope with burnout/over thinking?
I don't think this is the answer you're looking for, but I sleep.
I feel your next issue would be that period where sleep eludes you and you're just lying there and occasionally tossing and turning trying to find that one perfect sleeping position? And all those thoughts and feelings?
Listen to music, calming music not the *duf duf duf* music

That way as soon as your thoughts turn to "overthinking" or stress about the exam, just follow the music and let go of those thoughts

Normally if this happened to me I'd have a 20min playlist that stops after the last song (no loop). If I'm still awake after the playlist I'll get up, walk around a little and relax before going back to bed and starting the process (and the playlist) again.
Eventually you'll fall asleep and once you wake up you should feel much more better and refreshed!!
Good luck and stess less!
EDIT/disclaimer thing/pds thing
: This might not work for you. It works for me and usually I'm good after just one good night's sleep. However, you may prefer doing exercise (I quite like jogging but w/e) or maybe a favourite hobby will suffice to relax you (eg playing the guitar or watching tv for a bit)