New version, now we're getting closer:
When there are several abilities at the same time, first the current player resolves their abilities, and then each player in turn does.
However, you get a new chance to resolve a *Reaction* whenever a player after you resolves an ability: You could use a Reaction again (if it's still in your hand) or use one that you didn't use before.
Technically this means that each time a player resolves an ability (Reaction or otherwise), you start back with the first player, who again gets to use a Reaction. When a player doesn't resolve anything (Reactions or otherwise), continue with the next player in turn order. (If you choose to not use a Reaction because you want to see what the others do first, you risk that nobody else does anything and you don't get the opportunity to use it.)
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The important thing that is (hopefully) clarified here, which I don't think Donald's version did very well, is the following:
Player B has a mandatory and a Reaction, and does the Reaction. Now player A can do a Reaction - before player B does their mandatory. But player C cannot do a Reaction now; player B has to first do their mandatory.