I used this exact structure to deliver Brian's first piece of formal feedback not long after I took ownership of the team.
The initial result?
Brian went absolutely ballistic and told me that he had never heard such rubbish, and that he didn't know how I had been promoted to manager. He stormed out of the room and went home. He'd been allowed to continue with his patterns of behavior for such a long time that he had accepted them as normal.
However:
My senior manager told me that he'd support me every step of the way
My colleagues patted me on the back and told me it should have happened a long time ago
Start as you mean to go on in this new phase of your career. If you have any people like Brian in your team, please address them immediately, but remember that feedback can be painful for some. Stand your ground and work as hard as possible to keep to the principles illustrated in Chapter 1, Feedback Fundamentals. Data, facts, and evidence can still be uncomfortable to be presented...