Stillman shot and killed 13-year-old Adam Toledo following a foot chase two years ago.
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Carter's predecessor, David Brown, had only recommended a five-day suspension for the officer.
But, in documents filed with the Chicago Police Board, Carter said the officer violated seven department policies.
The Cook County State's Attorney has declined to press criminal charges in the case.
READ MORE | Adam Toledo shooting: Calls for justice continue 1 year after teen fatally shot by CPD