
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 $f(x) = \log_{a} \frac{1+x}{1-x}$ where $a > 0$ and $a \neq 1$,

(1) Determine the evenness or oddness of $f(x)$;

(2) If the domain of $f(x)$ is $[0, \frac{1}{2}]$ and its range is $[0, 1]$, find the value of $a$.

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