You can also use the word 'плащ' for 'coat' . We never used the word 'пальто' for coat.
Actually, пальто is used quite often. There also may be a slight difference, where пальто is used for a more heavy warm coat and плащ for a light one. But not everyone uses it like that.
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Мені пасує... Interesting that "me" acts as a third person singular here. If only i picked up a grammar book :D