I am also having a TON of issues with my gen 2 N7.... But I will list them later.
To answer your question, if your device memory is full, back up all personal files to your computer. Or you can back up your files to Google Drive. From there, do a factory reset. I highly doubt this will resolve your rebooting issues. Since I am also having the same issues. But it's a good place to start and everyone says to try that for your 1st or 2nd step in attempting to resolve your issues.
I had performed numerous factory resets. But unfortunately it did not fix my rebooting issue. I am still battling the rebooting issue about 3x a week. Happens randomly. I couldn't pinpoint why its happening.. But it does..
Recently another strange occurrence popped up. Played with the N7 before i went to bed. Woke up with the "Android Robot" and the black screen (similar to the robot icon as if you had updated the OS) that had the command prompt, "NO COMMAND" coming out of the robot's chest.... After numerous attempts to reboot the device, it finally came back to life... Business as usual... random reboots here and there.... But this morning, the device wouldn't power up.... but eventually it did... after numerous long presses on the power button.
Anyone faced the same problem(s)?? I am about to give up on this device! It had such high expectations! But lately, its been a major fail! Thank goodness I didn't buy the 32g! Otherwise I'd be slitting my wrists! Also, I tried to return my N7 back to Staples (purchased back in Nov '13) but they said they won't exchange it for a new one (outside the 30 day window), unless I had purchased Staples' warranty on electronic equipment. Only way for me to get a new one or possibly repair it is through Asus..
As much as I dislike Apple, I am HIGHLY considering jumping over to the Ipad Mini or Air!!!! Thank goodness I only wasted $200 on this paperweight!