I’m working on my own homebrew rpg system which I want to keep light on rules. Therefore I add only rules when they are needed. One rule which I did not use was an implementation of "initiative".
In combat, everyone’s actions happen at the same time. There is no order imposed by stats, dice rolls, or activity chosen, i.e. no initiative scores or initiative rolls such as in DnD 5e. It is more like melee from Warhammer Fantasy (the strategy game, not the rpg).
I did like the feeling in general during playtest, however management of combat turns was very chaotic, since I could obviously not do all the adjudication at the same time.
My question therefore is: What mechanics, tools, and techniques can I use to facilitate combat adjudication without imposing an order of action? I prefer answers referencing published RPG systems. Nonmechanical concepts should work without the use of online tools / software.