TORONTO, Sept 16 (Reuters) - Canada's main stock index advanced on Monday after investors were encouraged that Lawrence Summers had quit the race to become the U.S. Federal Reserve chairman and a deal was struck between Russia and the United States over Syria. The Toronto Stock Exchange's S&P/TSX composite index unofficially closed up 93.48 points, or 0.73 percent, at 12,816.88. All of the 10 main sectors on the index were higher.