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But he promised to lead the nation in an expansive agenda laid out during the most intense presidential campaign in history. In his address, he even promised to “harness the sun and the winds and the soil” part of a solution to the nation’s energy woes.

While giving his address, Mr. Obama looked out on a crowd that stretched from the steps beneath him out past the Washington Monument to the Lincoln Memorial and that appeared to shimmer as hundreds of thousands of flags waved in a pale winter sunlight.

After a lunch with his former congressional colleagues, he made his way from the Capitol to his new home at the White House, thrilling the giant crowds lining Pennsylvania Avenue by getting out of his motorcade and walking part of the way, hand in hand with his wife, capping a day of adoring crowds.

“I knew it was going to be crowded, but I couldn’t miss this,” said Adrienn Chu of the District’s Columbia Heights neighborhood.

Connie Grant of Birmingham, Ala., said she got up at 3:30 a.m. to try to make her way to the Mall and was still trying three hours later, but she said that didn’t matter. “I sacrificed and came here. To me, this is very historic. I just wanted to be here,” she said.

Southeast resident Ja-lene Willis said, “I had tears running halfway [down my face]. I’m so proud to be an American.”

Minutes before Mr. Obama took his oath of office, Vice President Joseph R. Biden Jr. was sworn in by Justice John Paul Stevens.

That went off without any problem, but with Mr. Obama, Chief Justice Roberts bungled the oath, misplacing the word “faithfully” in his first go-around. Mr. Obama waited for the chief justice to correct himself before proceeding.

At the congressional lunch, Mr. Obama made sure to find Chief Justice Roberts in the room and shook hands with him. They appeared to be joking about the botched oath, with Mr. Obama pointing back and forth between himself and the chief justice.

In brief remarks at the lunch, Mr. Obama demanded hard work of his former congressional colleagues, telling them that together they must live up to the unity that Americans have demonstrated on Tuesday.

“By being here today and by participating in innumerable ways across cities and small towns and suburbs all across the country, they are demonstrating their readiness to answer history’s call and to step up and give back and take responsibility for serving the common purpose of remaking our nation,” Mr. Obama told congressional leaders.

Mr. Obama’s inauguration marks the passing of leadership from one generation — his two predecessors are both 62 years old — to a more youthful one. The new president turned 47 on Aug. 4.

And while both Mr. Bush and President Clinton declared a desire to limit government, yet oversaw its expansion, Mr. Obama said Americans must pose a new question to government.

“The question we ask today is not whether our government is too big or too small, but whether it works — whether it helps families find jobs at a decent wage, care they can afford, a retirement that is dignified,” he said. “Where the answer is yes, we intend to move forward. Where the answer is no, programs will end.”

In his inaugural address Mr. Obama combined grim words about the nation’s situation with soaring rhetoric about its possibilities. His references to his historic achievement as the first black president were subtle, but his call for unity was clear.

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