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MIAMI (CBSMiami/AP) — Michael Bloomberg sees a chance in presidential politics after Hillary Clinton’s defeat and Donald Trump’s victory in New Hampshire.

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But those close to the former New York City mayor caution that he’s not rushing to join the race.

Bloomberg — widely considered a fiscal conservative but social liberal — has taken the first steps to mount an independent campaign. If he runs, he’d be looking to tap interest among middle-of-the-road voters in an election year dominated by candidates supported by those on the fringes of their parties.

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But even as Trump and self-described “democratic socialist” Bernie Sanders emerged victorious in New Hampshire Tuesday, Bloomberg’s aides suggested that Clinton’s shortfall may not be enough to compel his third-party run.

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