What primary role do Justices of the Supreme Court serve?

The primary role that Justices of the Supreme Court serve is judicial review. This process allows the Supreme Court to examine laws and executive actions to determine whether they are in accordance with the Constitution. Through judicial review, the Court plays a crucial role in upholding the rule of law, ensuring that legislation and government actions do not violate constitutional rights or principles. This authority is foundational to the American legal system and serves as a check on the legislative and executive branches of government, maintaining the balance of power among them.

The other options, such as legislative advisory, executive supervision, and public advocacy, do not accurately capture the core function of the Supreme Court justices. They do not engage in advising the legislature, overseeing executive actions, or advocating for public issues in the way suggested. Instead, their primary responsibility lies in interpreting the law and making definitive judgments that impact the law's application and its alignment with the Constitution.