You've got a 2006, so if you have the tranny temp gauge, you have the big tow package. Don't try to tow that much weight in anything other than 4th. ESPECIALLY if you're in hills/mountains. 4th is your gear, and as has been stated drop it manually into 3rd on steeper grades. This will help your trans stay cooler.
As for tow mode, use it too. It will help you get that much weight up to suitable towing speeds more easily without putting too much additional stress on the drivetrain.
You just can't be afraid to let the engine rev up with that much behind you when you're climbing the mountains. Your gas mileage will suck pretty bad though! Expect about 6 mpg.
