By Trevor Hunnicutt, Tim Kelly and John Geddie TOKYO (Reuters) -U.S. President Donald Trump lavished praise on Japan's first female leader Sanae Takaichi in Tokyo on Tuesday, welcoming her pledge to accelerate a military buildup and signing deals on trade and rare earths. Takaichi, a protegee of Trump's late friend and golfing buddy Japanese leader Shinzo Abe, applauded Trump's push to resolve global conflicts, vowing to nominate him for the Nobel Peace Prize, according to Trump's spokeswoman, Karoline Leavitt. Both governments released a list of projects in the areas of energy, artificial intelligence and critical minerals in which Japanese companies are eyeing investments of up to $400 billion. Tokyo pledged to provide $550 billion of strategic U.S. investments, loans and guarantees earl

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