Maybe I'm being excessively nit-picky here but I think you are getting stuck on the word purpose and forgetting that, as another person pointed out, it is just a word. What if you, instead, think about your "reason" for being here. Or maybe you can find a better word.
My point is this... You can construct your own purpose or reason to go on living. My belief is that there is NO PURPOSE to anything. We were not created or put here for any reason. A few molecules accidentally formed in such a way that increased their chances of survival and improved their ability to make copies of themselves. Through countless mutations that further increased fitness, we have arrived at humans (among a lot of other species) and after us will be other species. There is no purpose to any of this.
But we can look at what cards life has dealt us and we can try to make the best of it. We can construct our own reasons to go on living. For some people it is being able to raise children that will live on after them. For others, it's that delicious piece of fudge in the kitchen. Whatever reason you find only has to work for you. There is no deity to tell you that you are right or wrong. There is only you. You have to look at the life you have ahead of you and ask, "what can I do in this life that will make it worth while?" I don't know what that is. There may be people for whom the best thing in life is the leaving of it. But I hope you can find something of value that you can grasp and hold on to. Something that you love, that you can return to, that gives you joy and excitement, that makes the world seem new and interesting.
If there is a purpose or a reason to keep on living, it's this; it's the thing you would really miss doing if you weren't around to do it. And if you don't have that, well, maybe it's time you looked for it.
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Never let the weeds get higher than the garden,
Always keep a sapphire in your mind.
(Tom Waits "Get Behind the Mule")