You have the right size nut, just visit your local auto parts store and get a set, make sure to get the long version to accept your long lugs, most will use this opportunity to swap them all out.
I have had this happen once, now I use a six point impact socket and hand fit it all the way to the bottom of the "chrome" AS nut before I start to spin, keep your tool in alignment and fully seated and the AS nuts will last forever, I remove my wheels twice per year for rotation and inspection, only have messed up 1 lug nut.
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