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The News & Observer, Takaaki Iwabu, Associated Press
Former House speaker and Republican presidential candidate Newt Gingrich speaks to students at Broughton High School in Raleigh, N.C., Monday, April 9, 2012. Gingrich stopped by Broughton in the afternoon as part of his campaign and talked about his five principles for a successful life.

RALEIGH, N.C. — Trailing Republican presidential candidate Newt Gingrich wrapped up the first day of a short swing through North Carolina by telling high school students he believes in "a politics of big solutions" to problems others believe are too big to fix well.

Speaking Monday to 500 students before classes ended at Raleigh's Broughton High School, the former U.S. speaker and onetime leader in GOP presidential polls said the current political system doesn't have the ability to adapt to change effectively.

"As the institutions have started to fail, the cost of trying to solve them is greater than the system can figure out. So people just keep avoiding change," said Gingrich, pointing to potential insolvency to Social Security and curbing health care costs as examples.

His ideas include considering a Social Security model of personal savings accounts — pointing to those in Chile's workforce — and expanding investments in brain-related research that he said could ultimately save trillions of dollars in health care costs over decades. Gingrich said leaders in Washington only want to make changes that aren't long-term fixes, such as raising the retirement age and cutting benefits for Social Security.

"This is not the way politics is normally run in this country," Gingrich said of his ideas, "but I think we need a politics of big solutions."

Gingrich, who also met with business owners and black conservatives and attended lunch at a Raleigh restaurant, campaigned in North Carolina a day after the Georgia Republican said he expects Mitt Romney to win the Republican nomination. Gingrich also said he'll stay in the race to influence the party's platform. The North Carolina primary is May 8 — four weeks from Tuesday.

"My view is there's no reason to concede anything," Gingrich told reporters at a news conference Monday after the event with black leaders.

Gingrich said over the weekend he has a little less than $4.5 million in campaign debt and he's operating on a shoestring budget. He has won primaries in South Carolina and Georgia but has failed to break through after momentum failed to materialize and former Pennsylvania Sen. Rick Santorum became Romney's chief rival in recent weeks.

Gingrich spent one day in North Carolina last week, speaking to Raleigh outlets before speaking at the University of North Carolina at Wilmington. He's expected to speak Tuesday in New Bern at a Craven County Republican Party event and then return Saturday to Greensboro for a tea party rally.

Romney and Santorum have yet to spend much time or money in North Carolina, although an independent political committee started running ads last week in Wilmington on behalf of Santorum. Romney is expected to hold fundraisers next week in Charlotte and Raleigh.

At Broughton High School, Gingrich sounded like he hadn't given up on his presidential ambitions, however, after one student told him to stop President Barack Obama's re-election bid. "How about you helping me get through the North Carolina primary and we'll work on Obama next after that," Gingrich told the student.

Gingrich promoted his energy independence program to produce 4 million additional barrels of oil a day in the United States as a way to protect national security, create jobs and generate royalties that could reduce the national debt.

When another student asked him if he had a more environmentally friendly program, Gingrich responded: "There are a lot of things that you can do for the environment, but I frankly believe that having an American natural gas and oil production that's large enough is so important for national security and economic reasons it's worth doing," he said.

He gave the students five principles for a successful and enjoyable life — dreaming big, learning every day and working hard among them. At the very least, it appears running for president has fit the bill of being enjoyable for Gingrich.

"This has been a very long and a very hard presidential campaign, but the truth is I would say six days out of seven, it's been fascinating," he said.