Let $x,$ $y,$ and $z$ be nonnegative real numbers such that $x + y + z = 1.$  Find the maximum value of $x + y^2 + z^3.$
Question:
Let $x,$ $y,$ and $z$ be nonnegative real numbers such that $x + y + z = 1.$  Find the maximum value of $x + y^2 + z^3.$
Answer:
Let's think step by step.

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Let $x,$ $y,$ and $z$ be nonnegative real numbers such that $x + y + z = 1.$  Find the maximum value of $x + y^2 + z^3.$
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