2012 Chevy Silverado LTZ 5.3L V8 with 3.42 rear ax

[kipwachal]

Hi, we are thinking about buying the Crossroads Sunset Trail Reserve 32BH but need to confirm my 2012 Chevy Silverado 1500 LTZ 5.3L V8 with rear axle 3.42 will work. I was told by my local GM dealer that the LTZ has heavy duty cooling package and max towing capacity is 9500 lbs. The dry weight of the trailer is 7204.Any help with be greatly appreciated. Thanks!