86 If $p, q$ are the maximum and minimum values of the function $f(x)=-2 x+3$ on $|x| \leqslant 2$, then the maximum value of the function $g(x)=-\frac{2}{7} p x^{2}+q x-12$ on $|x| \leqslant 1$ is $\qquad$ .
$86-\frac{95}{8}$. According to the problem, we have
$$
\begin{array}{l}
p=f(-2)=-2(-2)+3=7, \\
q=f(2)=-2 \times 2+3=-1 .
\end{array}
$$

Therefore,
$$
\begin{aligned}
g(x) & =-\frac{2}{7} \times 7 x^{2}+(-1) x-12 \\
& =-2 x^{2}-x-12 \\
& =-2\left(x+\frac{1}{4}\right)^{2}-\frac{95}{8} .
\end{aligned}
$$

When $x=-\frac{1}{4}$, $g(x)$ reaches its maximum value $-\frac{95}{8}$.