How I resolved a clash between an HVAC duct and the structure before closing the ceiling

In my day-to-day, I handle MEP coordination on-site with ducts, sprinklers, cable trays, and framing. The problem that made me stop was this: a main duct was clashing with a beam, and the plan didn't show a clear alternative. The symptom that made me investigate it seriously was that the installer wanted to lower the duct, but that would break the clearance height and affect the diffusers. I…