Real numbers $x$, $y$, and $z$ satisfy the following equality: 
\[4(x+y+z) = x^2 + y^2 + z^2\] 
Let $M$ be the maximum of $xy + yz + zx$, and let $m$ be the minimum of $xy + yz + zx$. Find $M + 10m$.

Let's think step by step and output the final answer within \boxed{}.
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