Offer to take several random synths as ambassadors. The collective does not know how many, or of which color, but understands that not only will their common knowledge of other beings grow, their own will be saved.

“At least one of you is red”

They will all assume that they are the red one because they see no other red ones, but since that assumption is wrong, they will not shut down. They will discover that this is a lie and just assume that the intruder is a liar.