Let \( 1 < a < 7 \) and \( b > 7 \). If both mean and median of the data set \( \{1, 7, -7, a, b\} \) are equal to 4, then the value of \( b \) is _____.
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When dealing with both mean and median, always use the median to fix the middle value of your sorted list first. This usually determines one variable immediately, making the mean calculation much simpler.