Since you don't have the max tow package, your truck is probably 9200lbs since you have the 6 speed and 3:42 gears.
My 2018 CC 6.5' bed 6.2 4x4 has the 8 speed and the max tow package with 3:42 gears. Normal gearing with 8L90 is 3:23.
Max tow package and 6 speed you get 3:73 gears.
My tow rating is 11,800. I wound never want to tow that much with a half ton. Like others have said, tow 75% or less of what it is rated for. If your truck is rated at 9200lbs it should tow 7000lbs ok, especially with a weight distribution hitch.