Advancing Justice for Servicemembers Act This bill requires authorized officials to ensure procedures and requirements for a complaint are completed within 180 days after the complaint is received for complaints from members of the Armed Forces related to harassment or prohibited discrimination. If an authorized official does not take final action on a harassment or prohibited discrimination complaint within 180 days or provide the member a written explanation of the final action in relation to the complaint, a member of the Armed Forces may seek a court order directing the military department concerned to take final action or provide a written explanation.