(6) Let the function $f(x)=\log _{a}(x-3 a)(a>0, a \neq 1)$, when point $P(x, y)$ is a point on the graph of the function $y=$ $f(x)$, point $Q(x-2 a,-y)$ is a point on the graph of the function $y=g(x)$.
(1) Write the analytical expression for the function $y=g(x)$;
(2) If for $x \in[a+2, a+3]$, it is always true that $|f(x)-g(x)| \leqslant 1$, determine the range of values for $a$.
(6) (1) $y=g(x)=$
$\log _{a} \frac{1}{x-a}$
(2) $0<a \leqslant \frac{9-\sqrt{57}}{12}$