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Four fair coins appear in front of you. You flip all four at once and observe the outcomes of the coins. After seeing the outcomes, you select any pair of coins to reconsider. One of the two coins can be turned over, while the other must be flipped again. If you already have 3 3 heads, you still must perform both actions. You iterate this process until you end up with all 4 4 coins being heads. A movement of a coin is when you either turn over or flip it. Find the expected number of coin movements needed to obtain 4 4 heads.
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