This is a pretty cool idea, and I like the visual style as well.
I can't tell if the symbol selection is completely random or if it's somehow ensured there's a fair balance, since often I feel like I'm simply moving back and forth between the same symbols and I can't really be “clever” and do the right thing, I have to also be “lucky”.
At least you have three symbols to choose from, so there is room for some strategy.
I didn't get to the end because the “Levels” button seemed like a level selection (I wanted to check how many there are) but instead it throws you back to the title screen and you have to start over.
Good luck in the jam!