Turing Machine - Analyze brackets
It sounds like the only thing you care about is whether the number of open brackets equals the number of close brackets. In which case, I'd recommend an algorithm something like this:


Look for an open bracket.


If you can't find one, look for a close bracket.


If you find one, reject. Otherwise, accept.

If you can find one, erase it.

Look for a close bracket.


If you can't find one, reject.
If you can find one, erase it.



The exact mechanics of searching for brackets are up to you, but if you need more guidance, I'd recommend using one of your spare symbols ($E$ for empty) to mark empty patches of tape (everything to either side of the input) and the other ($B$ for bracket deleted) to mark things you've erased. That way you can tell when you reach the edge of the input string.