Let $x,$ $y,$ $z$ be real numbers such that $x + 2y + z = 4.$  Find the maximum value of
\[xy + xz + yz.\]
Question:
Let $x,$ $y,$ $z$ be real numbers such that $x + 2y + z = 4.$  Find the maximum value of
\[xy + xz + yz.\]
Answer:
Let's think step by step.

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4
Let $x,$ $y,$ $z$ be real numbers such that $x + 2y + z = 4.$  Find the maximum value of
\[xy + xz + yz.\]
train