BEIJING, Oct 27 (Reuters) – U.S. President Donald Trump faces one of the toughest challenges of his second term when he meets Chinese President Xi Jinping in South Korea on Thursday, where the world's two largest economies will seek to avert an escalation of their trade war. Washington and Beijing have raised tariffs on each other's exports and threatened to halt trade involving critical minerals and technologies. Neither side expects a breakthrough that would restore terms of trade that existed before Trump's second-term inauguration in January. Talks between the two sides to prepare for the meeting focused on managing disagreements and modest improvements, before a visit by Trump to China that is expected to happen early next year. RARE EARTHS China has vastly expanded its rare earths ex

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