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No you don't need a visa.
You can enter for 90 calendar days in any 180-day period on either your Schengen or USA visa.
Aliens holding a visa and/or a residence permit of any country listed above may enter and stay in Georgia without visa for 90 calendar days in any 180-day period.
For the purpose of entering and staying in Georgia without visa, a visa and/or a residence permit of a respective country shall be valid on the day of entry into Georgia (crossing the border), which must be evidenced by a travel and/or other appropriate document.