60 day notice on move out

I live in an apartment in Texas, me and my roomate just looked at our lease yesterday and realised that our apartment requires 60 day notice of move out. However we need to move out by the end of August which is when our lease is suposed to end.

Looking at the lease today, in paragraph 37 it states on moving out that:

"• If we require you to give us more than 30 days written notice to
move-out before the end of the lease term, we will give you a
written reminder not less than 5 days nor more than 90 days
before your deadline for giving us your written move-out. If we
fail to provide a reminder notice, 30 days written notice to moveout
is required."

They haven't given us a notice on our renewal at all, so does this mean that we can still put in our notice and not have to do a renewal month to month?

It appears so. Confirm this with management.