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* Japan shares look undervalued given record profits-analyst * Investors still wary after Nikkei's underperformance this year * Softbank gains on report it is seeking stake in Line Corp By Hideyuki Sano TOKYO, Feb 25 (Reuters) - The Nikkei average advanced to a 3-1/2-week peak on Tuesday after a rally in Wall Street shares to historic highs triggered short-covering in battered Japanese stocks. Shares of Softbank Corp climbed to their highest in a month on a report that the company is seeking to buy a stake in Line Corp, a mobile-messaging service controlled by South Korea's Naver Corp. The Nikkei was up 1.2 percent at 15,013.29 as of 0208 GMT after touching 15,079.84, its highest since Jan. 31. The benchmark has recovered about 40 percent of its losses since it fell from a six-year peak hit in late December. "The market looks fairly cheap considering that Japanese corporate profits are expected to hit record highs in the year to March and are expected to rise further in the following financial year," said Ryota Sakagami, chief strategist at SMBC Nikko Securities. "Historically, it is highly unlikely that Japanese companies would revise down their profit estimates when the U.S. economy is strong and when the currency market is stable," he added. The S&P 500 index hit an intraday record high on Monday as investors shrugged off a series of soft U.S. data as distorted by bad weather. The Japanese currency has stayed not far from five-year lows, with the dollar trading around 102.50 yen on Tuesday. Yet many investors remain cautious about chasing the market higher given Japanese shares' underperformance so far this year. The Nikkei is still down 7.5 percent in the year to date. "Today's buying was driven more by unwinding of existing (short) positions than fresh buying. I think it will take some time before investors' appetites warm up," said Masato Futoi, head of cash equity trading at Tokai Tokyo Securities. The gains were broad-based, with all of the Tokyo Stock Exchange's 33 subindexes rising. Softbank shares rose 4.1 percent, hitting a four-week high, after Bloomberg reported that Japan's third-largest mobile carrier was seeking to buy a state in Line. The broader Topix index rose 1.1 percent to 1231.89, though it stopped short of breaking above Monday's high of 1234.30. The JPX-Nikkei Index 400, an index launched this year comprised of firms with high return on equity and strong corporate governance, rose 1.0 percent.