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Usually people wear fancy or party clothes to celebrate New Year's, like a suit, a nice dress or something more dressed up than usual. Many go for black or gold clothes for the occasion, though honestly it depends on the type of event you're going to. If it's a party at a friend's place it can be more relaxed, but if it's somewhere fancy people put on their best outfits.
I personally always dress up a bit nicer for New Year's, like with a good pair of pants and a shirt, nothing over the top but something that shows you made an effort. The truth is it really depends on what your plans are that day, because if it's a party at someone's place or at a bar, obviously you dress more formal, but if it's more relaxed with family at home, you can go more comfortable. Either way, most people look for something that's not their everyday clothes, something that makes you feel special to say goodbye to the year.
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