GVWR has zero to do with towing capacity. It is how much the truck and anything you put in it and on it can ever weigh. This number does include the tongue weight but nothing else to do with the trailer. GCWR is the combination of GVWR ( the truck and all contents ) + anything you want to tow.
What you need to do is get your truck weighed with full tank of gas, and the weight of everything you plan to carry in the truck - people, gear, etc. Subtract this combined number from the GCWR of 23,000 and that the max you can realistically tow.