Let $x,$ $y,$ and $z$ be positive real numbers such that $xy + xz + yz = 1.$  Find the minimum value of $10x^2 + 10y^2 + z^2.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $x,$ $y,$ and $z$ be positive real numbers such that $xy + xz + yz = 1.$  Find the minimum value of $10x^2 + 10y^2 + z^2.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
4
Let $x,$ $y,$ and $z$ be positive real numbers such that $xy + xz + yz = 1.$  Find the minimum value of $10x^2 + 10y^2 + z^2.$
train