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Australia were set a target of 583 to win the second Ashes Test at Lord's on Sunday.
England declared their second innings on 349 for seven early on the fourth morning after Joe Root, 178 not out overnight, holed out for a superb 180.
If Australia were to reach their imposing target it would be a new record as no side has made more to win in the fourth innings of a Test than the West Indies' 418 for seven against Australia at St John's in 2002/03.
Ashes-holders England lead this five-match series 1-0 after their 14-run win at Trent Bridge last week.