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Supreme Court has 29 opinions remaining in one-month sprint to end controversial term

(CNN) As the Supreme Court rounds the final weeks of the term it has yet to decide an unusually high number of cases including disputes over abortion, gun rights, religious liberty, immigration and the environment -- issues that deeply divide the public and exacerbate the ideological split on the 6-3 conservative-liberal court.

June is always a fraught time at the court, as several justices have openly acknowledged in speeches over the years. But this spring is different. Not only are the nine judges reshaping contours of social issues that drive the public debate, but they are also working to salvage the institutional legitimacy of their own branch of government.

The court released one opinion Wednesday -- on a case involving a US Border Patrol agent -- and has 29 remaining.

In addition, the justices are dealing with unprecedented turmoil triggered by an internal investigation. Last month, Chief Justice John Roberts ordered the Marshal of the Court to find the person who breached internal protocols and leaked the draft opinion that would reverse Roe v. Wade that had been circulating among chambers.

As a result, according to CNN's exclusive reporting, the court has taken steps to require law clerks to provide cell phone records and sign affidavits. The process will distract the court from its duties and sow uncertainty -- even paranoia.

The leak, that Roberts himself called "absolutely appalling," has rattled the justices' faith in their ability to deliberate. Justice Clarence Thomas -- the conservative leader of the court -- told an audience last month that justices are now looking over their shoulders, shaken by the breakdown of their institution. He compared the leak to an "infidelity."

Here are the highlights of the court's docket:

Abortion

It was Thomas, the longest serving justice on the current court, who likely assigned fellow conservative Justice Samuel Alito to write the draft majority opinion in Dobbs v. Jackson Women's Health Organization. The dispute concerns a Mississippi law that bans abortion after 15 weeks. The state is asking the justices to take the giant step of overturning Roe v. Wade, a seminal case decided in 1973 establishing a constitutional right to abortion before fetal viability which most experts say occurs now around 23-24 weeks of pregnancy.

At oral arguments, Mississippi Solicitor General Scott Stewart told the justices that Roe and a follow up decision from 1992 "haunt" the country.

At one time Mississippi's law was dismissed as blatantly unconstitutional, even by a conservative-leaning appellate court. But much has changed since then, including the fact that in December the justices allowed a six-week ban on abortions in Texas to remain in effect. Since then, red states, invigorated by the Supreme Court's conservative majority, have passed increasingly restrictive laws. Last month, for example, Oklahoma Republican Gov. Kevin Stitt signed a bill into law that bans abortions from the stage of "fertilization" and allows private citizens to sue anyone who helps a woman obtain the procedure.

In the draft opinion, Alito said that Roe "must be overruled." If the five-member majority holds, it will wipe away near 50-year-old precedent and change the landscape of women's reproductive health going forward.

Supporters of abortion rights are clinging to the fact that Alito's opinion was a draft and hope it only reflects an opening salvo written after the justices casted initial votes at conference.

Votes can change during deliberations. Sometimes majority opinions fizzle into concurrences or even dissents. Other justices could be simultaneously working on separate opinions, hoping to pick off votes from Alito's draft or to weaken the thrust of his opinion.

Second Amendment

As the country grapples with gun violence, the justices will decide how broadly they want to rule in a case that could open up a new chapter in constitutional challenges to gun safety laws.

After oral arguments last year, it seemed the conservatives were ready to strike down a New York law -- enacted more than a century ago -- that places restrictions on carrying a concealed weapon outside the home. Supporters of gun rights have been pushing the court to clarify the scope of the Second Amendment for years. The effort has been led by Thomas who in the past called the Second Amendment a "disfavored right in this court."

But the entire landscape of the debate has shifted in recent months. Since the justices began deliberating, mass shootings have occurred across the country including a Texas massacre of 19 school children in Texas. While the shootings did not directly implicate the issue of concealed carry, the country as a whole is now debating gun safety laws.

Religious liberty

On top of abortion and gun rights, the court is also considering cases that could allow more religion in public life.

In December, they heard arguments concerning a Maine initiative that excludes some religious schools from a tuition assistance program. The program allows parents living in rural areas with no school district to use vouchers to send their children to public or private schools elsewhere. But it came under challenge when some parents wanted to use the vouchers to send their kids to religious schools.

The court could insist that if a state provides vouchers for public and private education, it cannot exclude schools that teach the curriculum through the lens of faith.

The justices are also grappling with the case of Joe Kennedy, a former Washington state high school football coach at a public school who lost his job for praying at the 50-yard line after games.

Kennedy told CNN that "every American should be able to have faith in public and not be worried about being fired over it."

"I think it is important to keep our promises -- especially to God," he said.

But the school district said it suspended Kennedy to avoid the appearance that the school was endorsing a particular faith, in violation of the Establishment Clause of the Constitution.

The liberal justices on the court -- Justices Stephen Breyer, Elena Kagan and Sonia Sotomayor --made clear at oral arguments that they were worried about players feeling coerced by the school to pray.

"I'm going to just sort of suggest," Kagan began "the idea of why the school can discipline him is that it puts some kind of undue pressure, a kind of coercion, on students to participate in religious activities when they may not wish to, when their religion is different or when they have no religion," she said.

Immigration

As the political branches spar over immigration, the justices are considering several cases concerning border disputes.

In one case, a group of Republican-led states are seeking to step in and defend a controversial Trump-era immigration policy, a version of which the Biden administration abandoned. The policy -- an expansion of the "public charge rule" -- has been excised by the Biden administration.

The case does not center on the legality of the rule, but, instead, whether the Biden administration followed proper procedures when it set out to revoke the rule and dismiss pending legal challenges. The Trump policy made it more difficult for immigrants to obtain legal status if they use certain public benefits such as Medicaid, food stamps and housing vouchers. The justices could reinvigorate legal challenges.

In a separate dispute, the justices are grappling with whether the Biden administration can terminate a Trump-era border policy known as "Remain in Mexico." Lower courts have so far blocked Biden from ending the policy.

Under the unprecedented program launched in 2019, the Department of Homeland Security can send certain-non Mexican citizens who entered the United States back to Mexico -- instead of detaining them or releasing them into the United States -- while their immigration proceedings played out. Critics call the policy inhumane and say it exposes asylum seekers with credible claims to dangerous and squalid conditions. The case raises questions not only regarding immigration law, but also a president's control over policy and his diplomatic relationships with neighboring countries.

Climate change

The justices unexpectedly also agreed to decide a case concerning the EPA's authority to regulate carbon emissions from existing power plants, in a dispute that could cripple the Biden administration's attempts to slash emissions. It comes at a moment when scientists are sounding alarms about the accelerating pace of global warming.

The court's decision to step in now concerned environmentalists because there is currently no rule in place. A lower court wiped away a Trump era rule in 2021 and the Biden administration's EPA is currently working on a new rule.

But the fact that there were enough votes to take up the issue now, struck some as an aggressive grant, signaling the court wants to limit the scope of the EPA's authority even before a new rule is on the books.

This story has been updated with additional developments.

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