Its basically like a cloud storage, and your local storage (your brain) gets wiped every loop. You can edit this file any time you want using your brain (you can be tied up and it still works). 1024 Bytes is all you get. Yes you read that right: BYTES, not KB, MB, or GB: 1024 BYTES
Lets just say, for this example: The loop is 7 days form a Monday 6 AM to the next Monday 5:59 AM.
How do you best use these 1024 Bytes to your advantage?
How would your strategy be different if every human on Earth also gets the same 1024 Bytes “memory buffer”?
How much time are you spending devising this system? Because you’re going to have to devise the system anew each week, unless you also store instructions for deciding on a system in the file.
How do you store what killed you? Theoretically you can’t edit the log once you die (you’d just start the new loop, with no memory of what killed you).
More importantly, why do you want to escape? This hypothetical time loop sounds awesome.