32. Given $3 a-2|b|=5, 4|a|-6 a=3 b$, then $a^{2}+b^{2}=$

Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.
Answer: 13.

Solution: From the given, we have
$$
3 a=2|b|+5>0,
$$

then
$$
3 b=4|a|-6 a=-2 a0, \quad b<0 \text {. }
$$

Thus, from the given equation, we get
$$
\left\{\begin{array}{l}
3 a+2 b=5 \\
-2 a=3 b
\end{array}\right. \text {, }
$$

Solving, we get
$$
\left\{\begin{array}{l}
a=3 \\
b=-2
\end{array},\right.
$$

Therefore,
$$
a^{2}+b^{2}=13 \text {. }
$$