Dec 13 (Reuters) - The Indian rupee pulled back from the day's low in afternoon trades on Tuesday as a rebound in local equities provided some comfort, though the outlook remained bearish, with shrinking domestic growth and Europe's debt worries weighing. * At 3:20 p.m., the partially convertible rupee was at 53.2800/2850 per dollar after touching an all time low of 53.52 earlier in the day. It had closed down 1.5 percent on Monday at 52.84/85. * Local shares nudged higher after a three-day slide on expectations the central bank will shift its policy stance toward supporting growth from fighting inflation after a steep drop in factory output. * The outlook for the rupee, Asia's worst performing currency this year, remains bearish, and traders said, the next support for the rupee is seen at 53.75 per dollar. * The euro plumbed two-month lows in Asia on Tuesday while the Australian dollar sank closer to parity as rising disappointment over the European Union's summit prompted investors to position for possible downgrades of euro zone sovereign credit ratings. * India is vulnerable to portfolio outflows from the stock market after data on Monday showed October industrial output slumped 5.1 percent, the first drop in more than two years. * Last Friday, India slashed its full-year growth forecast amid slowing domestic and global demand and officials warned the government was facing a serious balance of trade problem. (Reporting by Shamik Paul; Editing by Harish Nambiar)

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