The first three words of what you quoted ("On its turn...") are the important bit here, not the part you bolded. (Though the theme is reiterated at the end of the bold part - "during its turn.") Legendary actions are not taken on the creature's turn, and thus the whole quoted section is completely irrelevant to them.As far as I can tell, according to RAW Slow has no effect whatsoever on Legendary Actions.
Personally I might rule that it reduced the number of them the creature could take by one, but that would be explicitly a house rule; there's absolutely no way to get that out of a literal reading of the spell's description.
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