
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 the function $f(x^{2}-1)= \log_{m} \frac{2-x^{2}}{x^{2}} (m > 1)$,
(1) Find the analytic expression of $f(x)$ and determine its parity;
(2) Compare $f(\ln \sqrt{e})$ with $f(\frac{1}{3})$ and provide the necessary reasoning.

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