We have an unlimited number of dice at our disposal. Let's roll the die. If the outcome is 1, 2, or 3, we stop; otherwise, if it is 4, 5, or 6, a corresponding number of dice are rolled. For example, if the first roll gives 5, then we roll 5 dice, and so on. This procedure continues for every rolled dice whose outcome is 4, 5, or 6. Let N denote the N-th round of rolls. What is the total expected value at the end of the N-th round of rolls?
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