RE : which key do I use, the one inside or outside of the parenthesis?
None of the above.
You product key is a 25 digits set. The set comprises of 5, 5 digit format.
xxxxx-xxxxx-xxxxx-xxxxx-xxxxx
You installed Win 8 Pro first, then upgraded to Win 8.1 Pro. Yes?
You did that 8.1 upgrade via Windows Store. Yes?
If yes to both of the above, you do NOT have a Win 8.1 Pro product key.
You have, instead, a Win 8 Pro product key.
Belarc Advisor should have that product key listed under Software Licenses heading.
RE : how do I go about reformatting my computer to do a fresh install of windows 8.1?
You will have to re-install Win 8 Pro then upgrade back to Win 8.1 Pro via Windows Store.
Since you have lost the Win 8 Pro disk, here is a link from Microsoft showing you how.
Have you Win 8 Pro product key ready.
http://windows.microsoft.com/en-us/windows-8/upgrade-product-key-only