The action that is MOST CLOSELY based on the idea of checks and balances within the U.S. government is:
The Supreme Court votes to approve the appointment of presidential cabinet members.
This is because it reflects the system of checks and balances established by the U.S. Constitution, where the Senate (part of the legislative branch) has the authority to confirm presidential appointments, including cabinet members, thus ensuring that no single branch of government has unchecked power. However, it is worth noting that the Supreme Court itself does not vote on cabinet appointments; instead, this is done by the Senate. The closest answer from the options provided is still related to the checks and balances concept.