Let $z$ be a complex number such that
\[z^5 + z^4 + 2z^3 + z^2 + z = 0.\]Find all possible values of $|z|.$

Enter all possible values, separated by commas.
<|im_start|>system
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<|im_start|>user
Let $z$ be a complex number such that
\[z^5 + z^4 + 2z^3 + z^2 + z = 0.\]Find all possible values of $|z|.$

Enter all possible values, separated by commas.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
0,1
Let $z$ be a complex number such that
\[z^5 + z^4 + 2z^3 + z^2 + z = 0.\]Find all possible values of $|z|.$

Enter all possible values, separated by commas.
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