Let $z$ be a complex number such that
\[z + \frac{1}{z} = 1.\]Find $z^3.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $z$ be a complex number such that
\[z + \frac{1}{z} = 1.\]Find $z^3.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-1
Let $z$ be a complex number such that
\[z + \frac{1}{z} = 1.\]Find $z^3.$
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