For real numbers $x,$ $y,$ and $z,$ find the minimum value of
\[2x^2 + 5y^2 + 2z^2 + 4xy - 4yz - 2z - 2x.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
For real numbers $x,$ $y,$ and $z,$ find the minimum value of
\[2x^2 + 5y^2 + 2z^2 + 4xy - 4yz - 2z - 2x.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-1
For real numbers $x,$ $y,$ and $z,$ find the minimum value of
\[2x^2 + 5y^2 + 2z^2 + 4xy - 4yz - 2z - 2x.\]
train