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Gov. Andrew M. Cuomo of New York on Tuesday cast himself and the state that he leads as progressive beacons and a bulwark against President Trump, taking the oath of office while standing on Ellis Island.

In his third inaugural address, Mr. Cuomo pledged to pursue a “new justice agenda” that would confront a “cancer” of hatred and division that he said threatened the nation.

Mr. Cuomo conspicuously avoided invoking the president by name, even as he sharply rebuked a federal government that he said “has sought to demonize our differences and make our diversity our greatest weakness rather than our greatest strength.”

“America’s only threat is from within: It is the growing division amongst us,” Mr. Cuomo said. New York, he vowed, would be “the light to lead the way through the darkness.”