This is fine, though completely random would have worked just as well. I think it is wise to accept this team because:
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I know it has at least my vote to succeed.
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I think spies are unlikely to reject this mission as it is the first one. If I’m wrong, at least I’ll know who the spies are.
I know you all can’t know I’m on the side of good, but I do and we should proceed with this plan even if you, for some reason, suspect some of us on the team.