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I am sorry to hear about this situation.
1) Counter-suing is not a good idea. By doing so, it is less likely that the complaining party would agree to withdraw the complaint. Also, this may force their hand to sue you within the time allotted.
2) The better way to go about doing so would be to contact the party directly and to request that they withdraw the notification in exchange for someone in your situation peacefully simply taking down the video. They may agree. If they do, then the withdraw of their notification may "void" the strike. However I am going to be honest here, you really do not seem to have much leverage to demand anything per se. This is all negotiation at this point.
3) The good news is that you need three copyright strikes to have the account terminated. One strike does not terminate it, although one may lose access to some features. BUT THIS MAY BE UNDONE either if the complainant withdraws their complaint (as in #2), or, the strike will naturally expire in six months, as long as you complete Copyright School and don’t receive another copyright strike in that time.
So there are two ways to go about doing this to void the strike:
a) ask them to remove the complaint, or
b) simply take the Copyright School option and wait for it to fall off after 6 months.
Counter-filing may simply force a suit.
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