On Asia trip, Obama makes the case for U.S. relevance - and his own BRISBANE, Australia - President Obama left Washington a week ago with sagging approval ratings on foreign policy, dragged down by a year of crises ranging from Islamic militants to Ebola to Ukrainian separatists. He'll return Sunday evening feeling rejuvenated after a swing through the Asia Pacific netted a potentially major deal with China on climate change and a renewed sense that the United States still holds sway on the major issues of the day. Obama's eight-day, three-nation tour won't turn public perception of his global leadership around on its own, and the outcome of the crises that have preoccupied his administration over the past year are very much still in doubt. But his jaunt through the Pacific Rim helped him to rediscover his voice and make a forceful case for his world view. And his concrete accomplishments on the trip, while modest, provided a rare chance to boast. In addition to getting China to reduce carbon emissions in a first-of-its-kind agreement, Obama will bring back to Washington a breakthrough plan with Beijing that could lead to the first major international tariff reduction in 17 years. He also announced new U.S. commitments - $3 billion to a United Nations fund to help developing countries deal with the effects of global warming, and the creation of a new Peace Corps bureau in Burma. Obama and his aides hope the trip sets the stage for his final two years in office, a time when two-term presidents traditionally turn more attention to foreign policy. The president delivered a 5,400-word speech at the University of Queensland here on Saturday - an address billed as a talk about U.S. leadership in the Asia Pacific, but one that touched a broad range of issues: security, economics, trade, climate change, gay rights, women's rights, health care and human rights. World leaders, including Obama and Putin, gather for a photo after a plenary session at the Group of 20 summit in Brisbane, Australia. "Our world is getting smaller," Obama said, emphasizing that the United States is determined to help shape events all the way across the globe. Standing in front of American and Australian flags, Obama then quoted local writer David Malouf: "In that shrinking of distance that is characteristic of our contemporary world, even the Pacific, largest of oceans, has become a lake." Asked about the broad nature of Obama's remarks, a senior administration official said the goal was to "underscore or highlight the agenda for the next two years. The bulk of the speech covered areas where we are going to continue to invest. Obama's critics have said the president has, despite his rhetoric, overseen a foreign policy that has diminished the role of the United States in global affairs and, by consequence, left a vacuum for more nefarious actors - Russia's Vladi­mir Putin, China's Xi Jinping, the Islamic State - to feel emboldened to expand their power and influence. But the president took on Xi directly during the first stop on his trip, a three-day visit to Beijing, and more than held his own. In addition to the climate and tariff deals, the U.S. and China hammered out an agreement to relax short-term visa restrictions for students, tourists and businesses to promote tourism. Obama's first bilateral meeting in Beijing was a symbolic rebuke to China - he met with Indonesia President Joko Widodo, who was elected this summer on an anti-corruption platform in a nation transitioning to democracy. Obama also took the opportunity at the 21-nation Asia Pacific Economic Forum (APEC) in Beijing to confront Putin. They chatted informally three times on the sidelines of the APEC meetings, speaking on Ebola, the Islamic State and the fighting in eastern Ukraine for a total of 15 to 20 minutes, White House aides said. They did not elaborate on the outcome of the talks, but it marked the first face-to-face interaction between Obama and Putin in five months. In his Queensland speech, Obama acknowledged that his critics have looked skeptically at his administration's self-proclaimed "pivot to Asia," a strategic shift of military, economic and diplomatic resources away from the Middle East and Europe. People question "whether America has the staying power to sustain it," Obama said. And it's true that in recent years pressing events around the world demand our attention. As the world's only superpower, the United States has unique responsibilities that we gladly embrace. He ticked off the international crises of the past year. "So, yes, we have a range of responsibilities," he said. It's a burden we gladly shoulder. In his second stop in Burma, Obama gave voice to American values such as free speech, democratic elections and tolerance for religious and ethnic diversity - a theme that human rights advocates have said has gotten short shrift in Obama's international agenda. He was greeted warmly by Burmese Nobel laureate Aung San Suu Kyi, who hugged him happily as he stood with her on her porch addressing the media. And Obama met with Vietnamese Prime Minister Nguyen Tan Dung in hopes of deepening ties with a fast-growing country that has, like Burma and other Southeast Asian nations, felt threatened by a rising China. Obama aides said the broader goal of the week was to make the point that the United States" Asia pivot is not aimed simply at growing America's influence in Asia, but also to enlist U.S. allies - and even some traditional adversaries - to increase Asia's role on the world stage in global problem-solving. Obama praised China, for example, for contributing $130 million to help fight Ebola. Feeling good about the trip, White House aides distributed e-mails full of positive news coverage, and the president himself appeared energized as he took the stage at Queensland to the soundtrack from his 2008 campaign, including Brooks and Dunn's "Only in America." In a bid to charm his audience, Obama noted that he had tweeted about a study on climate change conducted by the university last year to his 31 million Twitter followers. Obama now has 50 million followers. "Just bragging a little bit," the president said, though he acknowledged that his influence only goes so far. "I don't think that's quite as much as Lady Gaga," he noted, "but it's pretty good."