Final answer:
TRICARE is the government-sponsored program that provides coverage for active-duty service members of the armed forces (ADSM).
Step-by-step explanation:
The government-sponsored program that provides coverage for active-duty service members of the armed forces (ADSM) is TRICARE. TRICARE is a health insurance program for military personnel, retirees, and their families. It offers a variety of healthcare plans that cover different populations, including active-duty service members.