Towing a 3023 with V-6 a 2007 Trailblazer

I have read a lot of posts on here about towing and I want to see what you think about towing this 2005 3023 with a Trailblazer. I called the Colorado Springs dealer and they said I could tow anything in their inventory with this vehicle. I understand I will be sacrificing power but my question is will it be safe? I am going to Cleburne TX to pick the unit up and would appreciate your thoughts. I bought a prodigy brake controller and had a transmission cooler installed. The tow package said it can tow 4000lbs and handle a 400lb tw. It also said with a wd hitch it could handle 7600lbs and 760lb tw. Again, please let me know your thoughts. Thanks.

Eric Stone