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The procedure for hearing cases in the Supreme Court involves several stages, and it generally follows a structured process:

Petition for Certiorari:Most cases reach the Supreme Court through a petition for certiorari, where a party requests the Court to review a lower court's decision.The Court receives thousands of petitions but selects a small number for review.

Cert Pool:The cert pool is a system where law clerks from different justices work together to review and summarize petitions for certiorari.

Justices use these summaries to decide which cases to hear.

Granting Certiorari:If four or more justices vote to grant certiorari, the Court agrees to hear the case.

Briefing:After granting certiorari, the parties involved submit legal briefs presenting their arguments. This includes the petitioner's opening brief, the respondent's brief, and sometimes an amicus curiae (friend of the court) brief.

Oral Arguments:Attorneys for both sides present their cases before the Supreme Court justices during oral arguments.Justices may interrupt with questions to clarify or challenge arguments.

Conference:After oral arguments, the justices meet in a conference to discuss the case and cast their preliminary votes.

Opinion Writing:The justice assigned to write the majority opinion presents the main rationale for the decision.Justices who disagree may write dissenting opinions.

Decision Announcement:The Court releases its written opinions, and decisions are made public.

Opinions can be unanimous, majority, concurring, or dissenting.

Mandate:The Court issues a mandate to lower courts, instructing them on how to implement the decision.

It's important to note that not all cases go through this entire process. Some cases are resolved without full briefing and oral arguments. Additionally, the Court has discretion in selecting cases, and only a small percentage of petitions are granted certiorari. The procedures ensure a thorough and careful consideration of legal issues brought before the highest court in the United States.