Let $u,$ $v,$ $w$ be the roots of $z^3 = 1.$  Find $uv + uw + vw.$
<|im_start|>system
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<|im_start|>user
Let $u,$ $v,$ $w$ be the roots of $z^3 = 1.$  Find $uv + uw + vw.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
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Let $u,$ $v,$ $w$ be the roots of $z^3 = 1.$  Find $uv + uw + vw.$
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