The planes defined by
\begin{align*}
-x + cy + bz &= 0, \\
cx - y + az &= 0, \\
bx + ay - z &= 0
\end{align*}all contain the same line.  Find all possible values of
\[a^2 + b^2 + c^2 + 2abc.\]Enter all the possible values, separated by commas.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The planes defined by
\begin{align*}
-x + cy + bz &= 0, \\
cx - y + az &= 0, \\
bx + ay - z &= 0
\end{align*}all contain the same line.  Find all possible values of
\[a^2 + b^2 + c^2 + 2abc.\]Enter all the possible values, separated by commas.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1
The planes defined by
\begin{align*}
-x + cy + bz &= 0, \\
cx - y + az &= 0, \\
bx + ay - z &= 0
\end{align*}all contain the same line.  Find all possible values of
\[a^2 + b^2 + c^2 + 2abc.\]Enter all the possible values, separated by commas.
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