Final answer:
The Supreme Court can issue a writ of certiorari, review briefs and oral arguments before deciding in conference, and has the power to declare laws or actions unconstitutional.
Step-by-step explanation:
The Supreme Court has the authority to take various actions when presented with a case. One action is the issuance of a writ of certiorari, which is a request for judicial review by the Court and an order for a lower court to send its records for Supreme Court review. Secondly, if the Court agrees to hear a case, justices review briefs and listen to oral arguments before making a decision in conference. Lastly, the Court has the power to declare laws or actions unconstitutional, effectively interpreting the Constitution and shaping the law of the land. These actions are taken under its appellate jurisdiction or when it exercises original jurisdiction in cases such as those involving foreign diplomats or states.