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In short, the town, or rather Patriarch and Doc, are almost done for. Completely due to their own actions. I suggest we make a grand exit and deal with the mafia.
Lynx is our remaining Eclipse leader, and judging by everything, Tox and Sky are two Blues.
We hang Lynx to get rid of the Eclipse. At night, the killer will visit the Blues. We'll be left with 2 - 1 - 1 if he's lucky. If not, the town will be wiped out at night anyway. So this is our only chance.
If everything works out, we'll discuss further during the day. If you think the killer played well and deserves to win, that's fine. If not, he'll play on your side as a shooter.
Does that work?
Execute Lynx