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Ashwin played a vital role in drawing the third Test in Sydney, batting for 42.4 overs with an aching back alongside Vihari.
Defending champions England find themselves in a precarious spot after a washed out game and a heavy defeat against Australia, who have qualified for the Super Eight stage.
Wicketkeeper Paine played 35 Tests for Australia, including 23 as skipper after Steve Smith was stripped of the role following a ball-tampering scandal during the team's 2018 tour of South Africa.
Renee Ferguson, 47, had missed the deadline to file her case against her former employer by almost three years and was seeking an extension of time in the Federal Court.
On Wednesday, Cummins spoke for the first time since Langer's resignation, saying the team needed a 'new coaching style' for the future.
Carey was preferred to uncapped wicketkeeper Josh Inglis.
Paine, who was the only specialist wicketkeeper named in Australia's 15-man Ashes squad, is likely to be replaced by experienced white-ball wicketkeeper Alex Carey or Josh Inglis, both of whom were named in the recent Australia 'A' squad.
Being captain was the one thing that guaranteed the 36-year-old selection and he now faces a challenge to prove he deserves a spot behind the stumps.
The Tim Paine episode should serve as an eye-opener not only to current cricketers but also to aspiring ones as acts of indiscretion committed even in early life can come back to hound one at a later date.
With less than three weeks to go for the Ashes, Paine had tearfully relinquished the Test captaincy over the scandal on Friday, saying he deeply regretted the incident.
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