If \( a, b, c, \) and \( d \) are real numbers satisfying:
\[
\begin{align*}
a + b + c &= 7, \\
a + b + d &= 10, \\
a + c + d &= 15, \\
b + c + d &= 12,
\end{align*}
\]
what is \( ac + bd \)? Let's think step by step and output the final answer within \boxed{}.
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