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The Democratic presidential race has grown increasingly bitter and personal ahead of next week’s New York primary, and Thursday night’s debate in Brooklyn may be the clearest indication yet of how fractious the contest has become.

Hillary Clinton and Senator Bernie Sanders of Vermont have clashed in sometimes caustic terms in recent days: Mr. Sanders has questioned Mrs. Clinton’s judgment, and she has criticized the credibility of his policy ideas with obvious exasperation.

The only remaining debate scheduled between Mr. Sanders and Mrs. Clinton is likely to be an exacting test on both sides. Here are some of the dynamics to watch:

Can Sanders fight outside his comfort zone?

Mr. Sanders can be somewhat formulaic in debates and on the stump. He rails against Wall Street, declares that it is time to break up the big banks and get money out of politics, and argues that only a “political revolution” can change Washington.

Beyond that, Mr. Sanders has often evaded and even struggled with thorny questions of policy. In a long interview with The Daily News last week, he repeatedly bristled and dodged when pressed on national security and foreign policy issues, and even on the fine points of some of his core concerns, like banking reform.