$(10$ points$)$ An active low$-$back exoskeleton is shown in the left picture below. The designer says that the exoskeleton works by generating an extra force to support the external loads, leading to reduced low$-$back muscle forces and L$5$S$1$ joint compression forces. As an ergonomist, please use biomechanical modeling approach to quantitatively analyze how this exoskeleton unloads low$-$back muscle forces and L$5$S$1$ joint compression forces. All required data are shown in the right picture. Please calculate the forces with and without the exoskeleton. Suppose the force generated by the actuator is $F_A=50N,$ and its moment arm to the L $5$ S $1$ joint center is $a=12cm.$