Final answer:
The Navy Enlisted Advancement System falls under the authority designated by Congress to regulate naval forces, as part of their power to maintain a Navy.
Step-by-step explanation:
The entity responsible for Navy-wide administration of the Navy Enlisted Advancement System is provided for under the authority to 'make Rules for the Government and Regulation of the land and naval Forces,' as established by the U.S. Constitution. This authority is part of the constitutional mandate given to Congress 'To provide and maintain a Navy.' While the specific organizational structure or position responsible for the Navy Enlisted Advancement System may change over time, it ultimately falls under the purview of the Department of the Navy, which operates within the guidelines of federal law and military regulations.