
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 a function $f(\log_a x) = \frac{a(x^2 - 1)}{x(a^2 - 1)}$,  
(1) Find the expression for $f(x)$ and determine its parity (even or odd).  
(2) Determine the monotonicity of the function $f(x)$.  
(3) For $f(x)$, when $x\in (-1, 1)$, it always holds that $f(1-m) + f(1-m^2) < 0$. Find the range of values for $m$.

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