A gruelling and bitter presidential campaign that will reshape American politics for years to come concluded on Monday with a final, fevered dash across the country by two candidates presenting vastly different visions for the nation's future.

At a rally and concert in Philadelphia, Democrat Hillary Clinton stood before a crowd of tens of thousands of people near where the country's founders adopted the Declaration of Independence and framed the vote as a choice between unity and division.

"Throughout our history, generations of Americas just like us have come together to meet the tests of their time," she said. "Tomorrow we face the test of our time."

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Earlier in the day, Republican Donald Trump addressed supporters in the crucial swing state of Florida and delivered a message more combative than hopeful. "You have one magnificent chance to beat the corrupt system and deliver justice," Mr. Trump said. "Do not let this opportunity slip away."

As millions of Americans head to the polls on Tuesday, the lead-ership of the world's most powerful nation hangs in the balance. Mr. Trump has appealed to voters as a brash outsider intent on restoring the past and defeating perceived threats to the country's safety, identity and economy.

Ms. Clinton is the voice of continuity and experience, who aims to keep the country on the course set by President Barack Obama and emphasize its diversity as a strength.

With hours left until Election Day, Ms. Clinton is favoured to win and become the first female president in U.S. history. A final round of major national polls gave her a lead of between three and five percentage points over her rival. Early voting totals in key states also show a surge of participation by Latino voters, potentially lifting Ms. Clinton toward victory. But in a race that has defied expectation from the outset, anything remains possible.

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On Monday, stock markets around the world rallied as investors cheered the likelihood of a win by Ms. Clinton and the end of election-related uncertainty. A day earlier, James Comey, director of the U.S. Federal Bureau of Investigation, had reaffirmed his decision to conclude, with no charges, the probe into Ms. Clinton's use of a private e-mail server while secretary of state. On Oct. 28, Mr. Comey roiled the final days of the campaign with an unprecedented announcement that his investigators were reviewing a new batch of e-mails.

In Philadelphia on Monday, Bruce Springsteen, the American rock icon, appeared to rapturous cheers from the crowd, opening with a version of his classic anthem Thunder Road. Ms. Clinton has "a vision of America where everyone counts," he said. "That vision is essential to sustain."

Former president Bill Clinton and first lady Michelle Obama exhorted voters in stark terms to get to the polls on Tuesday. "If we stay home or we play around with a protest vote, then Hillary's opponent will win," Ms. Obama said. "End of story."

When he stepped up to the podium, Mr. Obama made a spirited case for Ms. Clinton. "The vicious, crazy attacks, the double standards applied to her – they're like nothing we've ever seen before," he said. But "she doesn't complain and she doesn't buckle." Then Mr. Obama took a swipe at Mr. Trump: "She will deliver, she won't just tweet."

Toward the conclusion of her remarks on Monday night, Ms. Clinton began to look forward. "We have to bridge the divides in our country," she said. "I regret deeply how angry the tone of the campaign became."

After Philadelphia, Ms. Clinton was scheduled to fly to North Carolina for a final rally at midnight as the campaigns raced to use each minute left to reach voters.

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On Monday, Mr. Trump made stops in Florida, North Carolina, Pennsylvania and New Hampshire. The final event on his campaign calendar was a late-night rally in Michigan, a state his campaign is attempting to wrest away from Ms. Clinton.

Mr. Trump's path to the presidency remains narrow. To reach the threshold of 270 Electoral College votes, he must hold all of the states currently leaning his way, including Utah, where his rhetoric on refugees and Muslims has alienated Mormon voters. Mr. Trump must also win all of the major swing states: Florida, North Carolina, and Ohio. Then he needs to seize a state or two from Ms. Clinton's camp, such as Pennsylvania or Michigan.

In a positive sign for Ms. Clinton's campaign, several states with early voting have reported record turnout. That includes states such as Florida and Nevada, where the number of Latinos voting has surged in comparison with the same period in 2012.

In recent days, Ms. Clinton has begun to talk about what happens after the election is over, emphasizing the need for healing following a rancorous contest that has left Americans weary and dispirited about the state of their politics.

Her campaign released a final advertisement on Monday set to reach 20 million viewers featuring Ms. Clinton speaking directly to the camera for two minutes. "Is America dark and divisive, or hopeful and inclusive?" she asks. "Everywhere I go people are refusing to be defined by fear and division."