
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
The function $f(x)=\log_{a}(x-3a)$ and the function $g(x)=\log_{a}\frac{1}{x-a}$ ($a>0$ and $a\neq 1$) are defined in the interval $[a+2, a+3]$.  
(1) Find the range of values for $a$.  
(2) If $|f(x)-g(x)|\leq 1$ holds for all $x$ in the interval $[a+2, a+3]$, find the range of values for $a$.

Present the answer in LaTex format: \boxed{Your answer}
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