As an officer at a state institution, it is your responsibility to protect the health and safety of the inmates in your care. In the given scenario, a duty to protect the inmate was clearly breached as the inmate was beaten and raped by three other inmates. As such, the officer has an obligation to investigate the incident, report it to their superiors, and take steps to ensure the safety of the inmate and other inmates.

To be successful in a court action, the plaintiff must show that the duty to protect the inmate was breached, and that the breach was the cause of the injury or harm suffered by the plaintiff. The plaintiff must also show that the injury was foreseeable, and that the defendant had knowledge of the risk of harm and was deliberately indifferent to it. Furthermore, the plaintiff must show that the violation of the duty to protect was the proximate cause of the injury suffered.