
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 $f(x) = \log_{3} \frac{1-x}{1+x}$.
(I) Find the domain of the function $f(x)$;
(II) Determine the parity (even or odd) of the function $f(x)$;
(III) When $x \in \left[-\frac{1}{2}, \frac{1}{2}\right]$, the function $g(x) = f(x)$, find the range of the function $g(x)$.

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