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PHILADELPHIA — Hillary Clinton, the first woman to lead a major American political party's presidential ticket, accepted the Democratic nomination Thursday night with an appeal for a more collaborative and unified nation in the face of domestic divisiveness and global uncertainty.

And she described her opponent, Republican nominee Donald Trump, as a self-absorbed and unstable leader antithetical to America's need for cool-headed and compassionate leadership.

"We have to decide whether we're going to work together so we can all rise together," she said in perhaps the most closely-watched speech of her quarter-decade in the public eye.

Clinton's call for cooperation represented a direct repudiation of Trump's assertion in his acceptance speech last week that "I alone can fix it."

"Americans don't say: 'I alone can fix it,'" Clinton said to cheers from the crowd at Wells Fargo Center. "We say: 'We'll fix it together.'"

Related: President Obama Heaps Praise on Hillary Clinton at DNC

Describing a country "at a moment of reckoning," Clinton nodded to some of the same problems that peppered the remarks of speakers at last week's Republican National Convention in Cleveland: the threat of terrorism, the stagnation of wages for many Americans, and the systemic violence that plagues many communities nationwide.

But Clinton, unlike her GOP foes, cited greater inclusion and tolerance as the antidotes to the nation's ills.

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Saying that Trump has taken his party "from 'Morning in America' to 'Midnight in America,'" she said the Republican nominee "wants us to fear the future and fear each other."

"In the end, it comes down to what Donald Trump doesn't get: that America is great – because America is good," she said.

At times echoing President Barack Obama's optimistic vision of the future in his address Wednesday night, Clinton painted a hopeful picture of American resolve, tolerance and progress.

Referencing the convention's theme, "Stronger Together," Clinton urged recognition of the nation's shared values in a message aimed not just at liberal Democrats still smarting from the defeat of Bernie Sanders, but at the nation as a whole.

Related: Chelsea Clinton: Mom a 'Fighter' Who 'Never, Ever Gives Up'

Early in her remarks, Clinton directly addressed backers of the Vermont senator, telling his fans "I want you to know, I've heard you. Your cause is our cause."

Clinton's address was interrupted periodically by Sanders supporters in the arena who yelled "No more war!" Her fans tried to drown out the hecklers with chants of "Hillary!"

The former senator and first lady appeared to acknowledge the perception of many voters that she is too guarded or artificial in her public appearances.

"The truth is, through all these years of public service, the “service” part has always come easier to me than the 'public' part," she said. "I get it that some people just don't know what to make of me."

And she made a direct appeal to Republicans and independents wary of Trump's fitness to serve as the commander in chief.

"He loses his cool at the slightest provocation," she said of Trump. "Imagine him in the Oval Office facing a real crisis. A man you can bait with a tweet is not a man we can trust with nuclear weapons."

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"America's strength doesn't come from lashing out. Strength relies on smarts, judgment, cool resolve, and the precise and strategic application of power," she added. "That's the kind of Commander-in-Chief I pledge to be."

Speaking in Iowa before Clinton's remarks, Trump blasted Democrats as describing a naive vision of a world that doesn't exist.

Clinton's journey to the presidential nomination began over nine years ago, when she announced her first White House run with the declaration "I'm in, and I'm in to win." After her unsuccessful and bitter primary run against then-Sen. Barack Obama, she served as his secretary of state, enjoying for a time some of the highest approval ratings of her long career in the public spotlight.

But lingering questions over her use of a private email server during her time at the State Department -- compiled with voters' suspicions about the Clinton administration scandals of the 1990s — erased much of that warmth for the former first lady, leaving Clinton with historically poor favorability among voters.

At last week’s Republican National Convention in Cleveland, loathing for Clinton was raw, with delegates chanting “Lock her up!” and even one prominent speaker, Dr. Ben Carson, drawing a parallel between Clinton and Lucifer.

But in November she will face the one political candidate viewed even more negatively than she is by the American electorate: GOP nominee Donald Trump.