The complex numbers $z$ and $w$ satisfy the system
\begin{align*}
z + \frac{20i}w &= 5+i, \\
w+\frac{12i}z &= -4+10i.
\end{align*}Find the smallest possible value of $\vert zw\vert^2$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The complex numbers $z$ and $w$ satisfy the system
\begin{align*}
z + \frac{20i}w &= 5+i, \\
w+\frac{12i}z &= -4+10i.
\end{align*}Find the smallest possible value of $\vert zw\vert^2$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
40
The complex numbers $z$ and $w$ satisfy the system
\begin{align*}
z + \frac{20i}w &= 5+i, \\
w+\frac{12i}z &= -4+10i.
\end{align*}Find the smallest possible value of $\vert zw\vert^2$.
train