Suppose that $x$ and $y$ are real numbers satisfying  \begin{align*}
4y - 4x^2 &= 1 \\
4x - 4y^2 &= 1.
\end{align*} What is $\dfrac{1}{x^3 + y^3}$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Suppose that $x$ and $y$ are real numbers satisfying  \begin{align*}
4y - 4x^2 &= 1 \\
4x - 4y^2 &= 1.
\end{align*} What is $\dfrac{1}{x^3 + y^3}$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
4
Suppose that $x$ and $y$ are real numbers satisfying  \begin{align*}
4y - 4x^2 &= 1 \\
4x - 4y^2 &= 1.
\end{align*} What is $\dfrac{1}{x^3 + y^3}$?
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