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By Saif Hameed BAGHDAD (Reuters) - Iraqi special forces advanced on central Tikrit on Thursday as U.S.-led coalition planes joined the largest offensive yet against Islamic State militants holding out in Saddam Hussein's home city. Coalition jets launched their first air strikes against Islamic State targets in Tikrit on Wednesday, coming off the sidelines to aid Iraqi forces against the Sunni Islamist militants. Underlying the complex web of loyalties behind the conflict, a senior U.S. general said Washington had demanded the withdrawal of Iranian-backed Shi'ite militias fighting alongside Iraq's government before agreeing to take part. Some of the militias are openly hostile to the United States and have targeted Americans in Iraq in the past, but the fight against Islamic State has put them on the same side.