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President Barack Obama and Republican presidential candidate Mitt Romney depart the stage after the debate at Lynn University in Boca Raton, Florida, on Monday, October 22. The third and final presidential debate focused on foreign policy. See the best photos from the second presidential debate.

Romney and Obama greet each other at the end of the debate Monday night.

Obama and Romney hug their wives on stage after the debate.

President Obama greets first lady Michelle Obama.

Romney gestures beside his wife, Ann, on Monday.

Romney and Obama participate in the debate moderated by Bob Schieffer of CBS News.

Obama makes a point on Monday. He criticized his opponent on a host of foreign policy issues -- claiming Romney had favored positions that would have hurt the United States.

Romney gestures during the debate. The Republican nominee said Obama's foreign affairs policies have made the United States less respected and more vulnerable.

Obama listens during the final presidential debate.

Obama reacts to statements by Romney on Monday.

Romney emphasizes a point during the debate.

Obama and Romney face off while Schieffer looks on.

Obama answers a question Monday.

Romney speaks during the debate.

Monday's debate promised to be among the most-watched 90 minutes of the entire 2012 presidential campaign.

Schieffer listens to the candidates' responses during the debate.

Obama looks to Schieffer while debating Romney.

Romney and Obama debate on stage. The final face-to-face showdown took place 15 days before the election.

Romney listens as Schieffer speaks during Monday night's debate.

Obama makes a point during the debate.

Obama listens as Romney responds to a question Monday.

Obama and Romney greet each other as they join Schieffer on stage.

Ann Romney, center, and other members of the Romney family take their seats.

Schieffer appears on stage prior to the debate Monday. He is CBS News' chief Washington correspondent and has been the host of the Sunday morning discussion show "Face the Nation" since 1991.

Co-chairmen Frank Fahrenkopf, left, and Mike McCurry of the Commission on Presidential Debates address the audience at Lynn University.

First lady Michelle Obama arrives for the debate.

Romney and his wife, Ann, sit backstage with their family before the start of Monday's debate with President Obama. It was the candidates' final showdown before Election Day on November 6. See the best photos from the second presidential debate.

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Watch a replay of Monday's presidential debate at 12:30 a.m. ET and CNN's exclusive expert analysis on CNN TV, CNN.com and CNN's mobile apps for iPhone, iPad and Android. Clip-and-share your favorite debate moments on Facebook and Twitter.

(CNN) -- A forceful President Barack Obama put Republican challenger Mitt Romney on the defensive on foreign policy on Monday night, with analysts and an immediate poll giving him the victory in the third and final debate just 15 days before the November 6 vote.

Obama displayed the experience of a commander-in-chief in explaining U.S. policy under his leadership and attacking the views and proposals of Romney, a former Massachusetts governor with less experience on international issues.

Romney ended up supporting most of the Obama administration's steps involving hotspots, such as the civil war in Syria, and preventing Iran from getting a nuclear weapon, giving the president the advantage in a debate in which his GOP rival needed to question foreign policy of the past four years.

Were your questions answered? Share your reactions to the final debate.

Analysts agreed that Obama won the debate on points, but questioned if the result would have a big impact on voters and the race as a whole ahead of Election Day.

"There's no question debate coaches would score this one for the president," said CNN Chief National Correspondent John King, while CNN Senior Political Analyst David Gergen said Obama "dominated the middle of the debate" and emerged as the winner.

Both King and Gergen agreed that Romney avoided sounding like an overzealous advocate of military action -- which is how Obama and Democrats seek to portray him.

Alex Castellanos, a Republican strategist and CNN contributor, conceded Obama "won tonight on points, no doubt about it," but added that Romney showed the cool and calm leadership style of a commander-in-chief to show that making a change in leadership now would be safe.

A CNN/ORC International poll of people who watched the debate showed 48% favored Obama compared to 40% for Obama, a result considered statistically even under the margin of error of plus-or-minus 4.5%. Another poll by CBS scored it a clear victory for Obama.

However, the CNN/ORC poll showed viewers thought Romney established credibility as a leader, which former White House Press Secretary Ari Fleischer, a Republican strategist and CNN contributor, said was very important.

"This isn't going to change the trajectory of the result," Fleischer said.

The third and final face-to-face showdown occurred with the candidates running even in national polls and the race hinging on a handful of battleground states -- particularly Ohio, Florida and Virginia.

According to the latest polls, Obama has a slight lead in Ohio. Romney is ahead in Florida, and Virginia is a dead heat.

Obama more than once sought to highlight Romney's lack of foreign policy experience, while Romney said Obama's foreign affairs policies have made the United States less respected and more vulnerable.

Romney also repeatedly tried to shift the discussion to his strongest issue -- the continued high unemployment and slow economic recovery under Obama -- arguing that a strong foreign policy and national defense depends on a strong economy.

The president's policies undercut the military, leaving the Navy and Air Force at their weakest levels in decades, Romney said.

"Our Navy is smaller now than at any time since 1917," the Republican nominee said, also noting that "our Air Force is older and smaller than at any time since it was founded in 1947."

Obama fired back with perhaps his strongest response of the night, saying Romney "maybe hasn't spent enough time looking at how our military works."

"You mentioned the Navy, for example, and that we have fewer ships than we did in 1916," Obama said. "Well, governor, we also have fewer horses and bayonets, because the nature of our military' has changed."

Sarcastically noting that the Navy now has "these things called aircraft carriers, where planes land on them." as well as "ships that go underwater, nuclear submarines," Obama concluded that "the question is not a game of Battleship, where we're counting ships -- it's what are our capabilities."

How foreign policy hits close to home

Romney applauded Obama's efforts to kill Osama bin Laden and other al Qaeda leaders but insisted that "we can't kill our way of this mess." Rather, he pushed for "a comprehensive strategy" to curb violent extremism in the Middle East.

"The key is the pathway is to get the Muslim world to reject extremism on its own," Romney said, proposing U.S. policies to promote economic development, better education, gender equity and to help create institutions.

However, he was unable to express any significant policy difference with Obama on how that would happen.

Obama responded by criticizing his opponent on a host of foreign policy issues -- claiming Romney had favored positions that would have hurt the United States or offered sometimes contradictory views.

"What we need to do with respect to the Middle East is strong, steady leadership -- not wrong and reckless leadership that is all over the map," the president said.

Read the full debate transcript

Romney's economic plan seeks trillions in tax cuts while increasing defense spending, which would increase the deficit, Obama said.

For his part, Romney repeatedly shifted back to his stump speech criticism of the nation's sluggish economic recovery under Obama's policies, which he says have hindered growth through high taxes and onerous regulations.

The candidates were at odds as well about how Washington should ultimately respond to the continuing violence in Syria.

Checking the candidates' facts on foreign policy and national security

Talking about the need to provide those fighting Syrian President Bashar al-Assad's forces with arms, Romney said the Democratic incumbent has not enough to curb violence that has left tens of thousands of people dead and also destabilized the region.

"We should be playing the leadership role," Romney said.

That precipitated a quick response from Obama, who pointed to American efforts to organize international efforts to address the issue as well as its support for opposition factions. "We are making sure that those we help will be our friends (in the future)," he said.

A strong performance by Romney against a lackluster Obama in the first debate October 3 in Denver helped the GOP challenger tighten the race and even pass the president in some polls.

Where they stand: Candidates and issues

The president fought back to win the second debate last week in New York, according to polls and pundits, setting up the Monday's night showdown at Lynn University in Boca Raton, Florida, moderated by CBS News Chief Washington Correspondent Bob Schieffer.

Until recently, polls showed Obama ahead of the former governor on foreign relations issues, and the Romney campaign has mounted pointed attacks in an attempt to narrow the president's advantage.

Other issues discussed in the debate included Iran's nuclear ambitions, China and the war in Afghanistan. Both candidates pledged to support Israel if the Jewish state comes under attack, and Romney backed the 2014 date set by Obama and NATO for withdrawing combat troops from Afghanistan.

Romney has landed blows thus far in the campaign by arguing that continued high unemployment and sluggish growth showed failed policies under the president, while promoting his own business background.

CNN/Google Campaign Explorer: Ads, money and travel

In a major foreign policy address on October 8, Romney promoted a traditional U.S. foreign policy dating back decades, based on exerting global influence through military and economic power. While the speech sought to distinguish himself from Obama on foreign policy, specific proposals he cited then were similar to what the administration is doing.

Obama's campaign has accused Romney of shifting positions on foreign policy matters and mishandling a trip to England, Israel and Poland this summer when he publicly questioned London's preparedness to host the Olympic Games and cited cultural differences as a reason for economic disparities between Israelis and Palestinians.

Defense: $2 trillion divides Obama and Romney

CNN's Greg Botelho contributed to this report.