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Chinas leader Xi Jinping met for the last time with U.S. President Joe Biden on Saturday but was already looking ahead to President-elect Donald Trump and his America first policies, saying Beijing is ready to work with a new U.S. administration.”During their talks on the sidelines of the annual Asia-Pacific Economic Cooperation summit, Xi cautioned that a stable China-U.S. relationship was critical not only to the two nations, but also the future and destiny of humanity.Make the wise choice, he cautioned. Keep exploring the right way for two major countries to get along well with each other.Without mentioning Trumps name, Xi appeared to signal his concern that the incoming presidents protectionist rhetoric on the campaign trail could send the U.S.-China relationship into another valley.China is ready to work with a new U.S. administration to maintain communication, expand cooperation and manage differences so as to strive for a steady transition of the China-U.S. relationship for the benefit of the two peoples, Xi said through an interpreter.Xi, who is firmly entrenched atop Chinas political hierarchy, spoke forcefully in his brief remarks before reporters. Biden, who is winding down more than 50 years of public service, talked in broader brushstrokes about where the relationship between the two countries has gone. He reflected not just on the past four years but on the decades the two have known each other.We havent always agreed, but our conversations have always been candid and always been frank. Weve never kidded one another, Biden said. These conversations prevent miscalculations, and they ensure the competition between our two countries will not veer into conflict.Biden was expected to urge Xi to dissuade North Korea from further deepening its support for Russias war on Ukraine. The leaders, with top aides surrounding them, gathered around a long rectangle of tables in an expansive conference room at Limas Defines Hotel and Conference Center.China hosted the meeting this year, after Xi and Biden met a year ago on the APEC sidelines in Northern California, a gathering hosted by the U.S. They had much to discuss, including Chinas indirect support for Russia, human rights issues, technology and Taiwan, the self-ruled democracy that Beijing claims as its own.Theres much uncertainty about what lies ahead in the U.S.-China relationship under Trump, who campaigned promising to levy 60% tariffs on Chinese imports.Already, many American companies, including Nike and eyewear retailer Warby Parker, have been diversifying their sourcing away from China. Shoe brand Steve Madden says it plans to cut imports from China by as much as 45% next year.In a congratulatory message to Trump after his victory over Vice President Kamala Harris, Xi called for the U.S. and China to manage their differences and get along in a new era. In front of the cameras Saturday, Xi spoke to Biden but it was unmistakable that his message was directed at Trump.In a major flourishing sci-tech revolution, neither decoupling nor supply chain disruption is a solution, Xi said. Only mutual, beneficial cooperation can lead to common development. Small yard, high fence is not what a major country should pursue.After he was greeted by Xi, Biden ignored shouted questions from reporters on his concerns about the incoming Trump administration as well as North Korea. The leaders also did not engage reporters after they made their brief comments at the start of the meeting.Biden administration officials would advise the Trump team that managing the intense competition with Beijing will likely be the most significant foreign policy challenge they will face, White House national security adviser Jake Sullivan said.Biden has viewed his relationship with Xi as among the most consequential on the international stage and put much effort into cultivating it. The two first got to know each other on travels across the U.S. and China when both were vice presidents, interactions that both have said left a lasting impression.For over a decade, you and I have spent many hours together, both here and in China and in between,” Biden said. Weve spent a long time dealing with these issues.But the last four years have presented a steady stream of difficult moments.The FBI this week offered new details of a federal investigation into Chinese government efforts to hack into U.S. telecommunications networks. The initial findings have revealed a broad and significant cyberespionage campaign aimed at stealing information from Americans who work in government and politics.U.S. intelligence officials also have assessed China has surged sales to Russia of machine tools, microelectronics and other technology that Moscow is using to produce missiles, tanks, aircraft and other weaponry for use in its war against Ukraine.And tensions flared last year after Biden ordered the shooting down of a Chinese spy balloon that traversed the United States.Biden is looking for Xi to step up Chinese engagement to prevent an already dangerous moment with North Korea from further escalating.Biden, South Korean President Yoon Seok Yul and Japanese Prime Minister Shigeru Ishiba on Friday condemned North Korean leader Kim Jong Uns decision to send thousands of troops to help Moscow repel Ukrainian forces who have seized territory in Russias Kursk border region.Biden called it dangerous and destabilizing cooperation.White House officials have expressed frustration with Beijing, which accounts for the vast majority of North Koreas trade, for not doing more to rein in Pyongyang.The North Koreans also have provided Russia with artillery and other munitions, according to U.S. and South Korean intelligence officials. And the U.S., Japan and South Korea have expressed alarm over Pyongyangs stepped-up cadence of ballistic missile tests.Kim ordered testing exercises in the lead-up to this months U.S. election and is claiming progress on efforts to build capability to strike the U.S. mainland.Xi and Biden started their day at the leaders retreat at the APEC summit, taking part in a photo where they all wore scarves made from vicua wool, a symbolic animal for Peru. Its common practice that leaders at these gatherings are given a gift usually traditional clothing of the host country that they don for the photo.___Long reported from Washington. Associated Press writer Mari Yamaguchi in Tokyo contributed to this report.