Let \( A = \begin{bmatrix} 0 & \alpha \\ 0 & 0 \end{bmatrix} \) and \( (A + I)^5 - 50A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \). Find \( abc + abd + bcd + acd \):
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When solving matrix problems, use matrix operations and properties to simplify the calculations.