
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
Let the function \( f(x)=\log _{a}(x-3 a) \) with \( a > 0 \) and \( a \neq 1 \). When the point \( P(x, y) \) is on the graph of the function \( y=f(x) \), the point \( Q(x-2 a,-y) \) is on the graph of the function \( y=g(x) \).
1. Find the expression for the function \( y=g(x) \);
2. If \( |f(x)-g(x)| \leqslant 1 \) always holds when \( x \in [a+2, a+3] \), determine the range of values for \( a \).

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