1. depend on the states, landlord has obligation to mitigate damage. But I know NY has no such requirement (that is, in NY, you are truely responsible for 10 months of rent), so you need to google "landlord obligation to mitigate damage in XX state".
and also google "how to break lease in XX state".
2. google notice of abandonment XX state, notice the format and waiting period.
3. Just because they ask you to do something doesn't mean you will do it. Everytime you do something you have to get something in return. such as: I will pay if you release me from the lease. Don't just do it without anything in return.
To terminate lease, google "mutual release from lease agreement".