Part of most contracts is that you have a so-called “cooling-off period”. What this means is that you have the option to back out of your current contract, and reconsider your needs. You may be able to add terms or adjust others that do not suit your needs. This needs to be done within a specified period of time. You may be aware of such terms for other contracts like your phone or electricity supplier, but some people are not aware that this is also the case for termination by mutual agreement.
Sadly, it is not as straightforward as having a “one rule fits all” solution when it comes to a termination by mutual agreement. Different US states have different laws and ways of regulating contracts. This means that even if you have experience with termination by mutual agreement in the workplace, but have moved state, you may need to get legal counsel to ensure you are taking the right steps.