How to turn on an Apple TV via HomeKit

This is about as basic an automation as it gets. I have an Apple TV and an LG TV added as accessories in a room Home Theater. The two devices are not directly connected (there’s a sound/video processor as the central point). I want to set an automation so that the tv turns on when I turn on the Apple TV via the remote on my phone. I can’t see how to use the Apple TV accessory as a trigger for the TV.

Ideas?