You are managing a work cell, which consists of two machines in series as depicted below $($the reliability of each machine is depicted in the boxes$).$ In addition, you procured a third machine with a reliability of $1$ to back up either Machine #$1$ or Machine #$2.$ You must back up one and only one of these machines by the third machine. Your decision of which the two machines to back up is guided by the goal of maximizing the reliability of the work cell. What might be the maximum reliability of the work cell that includes the backup machine?