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(Reuters) - The U.S. Federal Reserve should do all it can to reduce very high unemployment and bring inflation back up to more desirable levels, a top Fed official said on Monday.

"It's vital that we keep the monetary policy throttle wide open," John Williams, president of the San Francisco Federal Reserve Bank, told a group of students and professors at Claremont McKenna College.

"That will help lower unemployment a little bit quicker, and raise inflation back toward levels consistent with our mandates," he said. "And importantly, we want to do so quickly to minimize total economic damage.