"Let Anthony take care of it" simply meant Ange would hands-off, play on his own, and then be told what to do once Anthony had made the arrangements, colloquially known as 'delegate and disappear.'
Quietly shrinking and shrinking, Ange "quietly" slipped away—of course, this 'quietly' is in quotes. While everyone saw him sneak off, they all knew his character and couldn't be bothered to stop him.
After slipping out, Ange decided to go a bit further and flew into the depths of the Chaos Mist for a few minutes before stopping.
During the flight, Ange gathered all the Chaos Mist along his travel route, storing it inside his Dimensional Space.
In fact, ever since he materialized the Chaos Mist into sand, stone, and mud, Ange knew this substance must be consciousness-related because it couldn't undergo Element Conversion.
If it were matter and energy, he could convert it into something else, but mental powers were unconvertible.
