
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 \( 0 < a < 1 \), the function \( f(x) = \log_a \frac{x-3}{x+3} \) and \( g(x) = 1 + \log_a (x-1) \) have a common domain \( D \). If \( [m, n] \subset D \) and the range of \( f(x) \) on \( [m, n] (m < n) \) is \( [g(n), g(m)] \), determine the range of values for \( a \).

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