Hi,
there are many problems for me with this challenge.
One is that this particular question has been presented before a number of times, in various forms, and the memory of possible answers (or even the presentation) makes it hard for me ignore them and ponder on it myself. "Kaoru Yumi" (The Scented Darkness) from a manga I like - Mushishi - is beautifully presenting this question.
Another is that I when I have to deal with the concept of "time", I feel despair. What is time, really?
Then, I thought of working with pen and paper, so I drew a timeline and a time 'knot'. Drawing time as a line is not really clever, just immediate. Then, I drew the time loop as a circle, only because it was easier. But this presentation is faulty, because it makes you think exiting the loop can be done through the tangent point of the circle to the line. In reality, each completed loop represents an interval (of a certain length) which adds up on the timeline, until the end of your lifespan/timeline. Because you draw time as a line, the loop may still be there, but you're still on the timeline, because being in a loop doesn't "stop" time. So if I want to try to come up with a graphical solution for it, time must be represented differently.I'll try to maybe come up with something tomorrow...
Apart from this, breaking a cycle you're not aware of, or vaguely aware of, comes with other questions - why are you in that cycle? Is it maybe a choice - to lose yourself into a pocket of forgetfulness, for self-preservation? Or a refusal of time, seen as an oppressor, and choosing the living of a perpetual present?
I suppose the thrilling part is the one of sending messages to a past self that would trigger the creation of an ever more aware version of yourself with every passing of the loop, ultimately giving you the means of escaping the loop - and this can be done infinitely safer than addressing some of the questions above. Forgive this wall of text, but some questions come with a huge load and I write/talk a lot (so most of the time I shut up, making it look like I don't think at all hehe).