Final answer:
The judicial branch uses Judicial Review to determine the legality of other branches' actions, a power established by the case of Marbury v. Madison.
Step-by-step explanation:
The tool that the judicial branch must use to determine if an act of another branch is legal is C) Judicial Review. Judicial review is the power of courts to assess the constitutionality of actions taken by the legislative and executive branches. This power was established in the landmark case of Marbury v. Madison in 1803, which is not explicitly stated in the Constitution but has become a fundamental principle in the United States legal system. Through judicial review, the Supreme Court, as well as lower courts, can strike down laws passed by Congress or actions taken by the President if they are found to be unconstitutional. Although this power is exercised relatively infrequently, it is a critical mechanism for maintaining the system of checks and balances that is key to the operation of the U.S. government.