By Selim Algar, Julia Marsh and Kate Sheehy

Every school in the city should be engineered to match the exact racial mix of the city, and there should be no sorting by academic ability, an education panel handpicked by Mayor Bill de Blasio and Schools Chancellor Richard Carranza said yesterday.

The panel recommends redrawing school-district lines citywide to “fully integrate” them within 10 years.

Every Gifted & Talented program also should be scrapped, as well as nearly all screening processes — which admit students based on factors such as grades, behavior and attendance — to combat racial and socioeconomic inequality, according to a report issued Tuesday by the School Diversity Advisory Group.

Within three years, every city school should reflect its community in terms of diversity, the report said. In five years, it should reflect its entire borough.

And in 10 years, “every school should be representative of the city as a whole,” the panel said, emphasizing that the city Department of Education “should redraft district lines to support the long-term goal of having all schools reflect the city population,” the group wrote.