Change Worker's Primary Assignment and Delete the Old

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My goal is to create a new assignment for a worker and have that new assignment's primary flag set to 'True'. Once the new assignment is the primary, I want to delete the old assignment. Through trial and error I've been able to create a new assignment and change the 'PrimaryAssignmentFlag' but that doesn't seem to help achieve my goal as the old assignment is still considered the primary for the work relationship. Any ideas how to do this using only HCM APIs? Below I'll linked the APIs I've been working with to achieve my progress so far: