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Senator Rand Paul speaks at a session titled "The Changing Politics of Foreign Policy" during the Wall Street Journal's CEO Council meeting in Washington December 2, 2014. REUTERS

Sen. Rand Paul, R-Kentucky, who is considering his own run for the White House, poked fun at potential presidential contenders Jeb Bush and Mitt Romney on Facebook and Twitter over their meeting in Utah Thursday, joking that Bush gave Romney a "third time's a charm" bracelet, and Romney gave Bush a "common core" friendship band.

Their meeting had been planned for two weeks -- before Romney told donors he is considering another White House bid. It was described as a social, but it came at an awkward time, when each of them had begun to try to lock up the support of the same donors for a potential presidential run.

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Mitt Romney tops the latest CBS News poll, just days after hinting at another presidential bid. He's followed by Jeb Bush, Mike Huckabee, Sarah P...

The two, who had lunch in Salt Lake City Thursday, "did not reach an agreement...on how to reconcile their competing plans to run for the White House next year," the New York Times reported, citing advisers to Bush and Romney. And their lunch, the Times said, was "cordial" and "gentlemanly."

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Rand Paul pokes Romney and Bush