
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
Given that \(f(x) = \log_a \frac{1 - mx}{x - 1}\) is an odd function \((a > 1, a \neq 1)\),
(1) Find the value of \(m\);
(2) Based on the result from (1), determine the monotonicity of \(f(x)\) on \((1, +\infty)\) (proof not required);
(3) If the range of \(f(x)\) is exactly \((1, +\infty)\) when \(x \in (r, a-2)\), find the values of \(a\) and \(r\).

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