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I don't have time to find the REG quote, but when a limited-use artifact is used for the final time, it is immediately discarded. Therefore, it would be too late to DoN it.
Some artifacts, covenants, or curses have a limited number of times you can use them. When these come to an end, you must discard them immediately. Once such an artifact, covenant, or curse is activated, it must be counted as having been used. This is true even if other events duplicate the effect of the artifac, covenant, or curse during the turn.