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

(1) Find the domain of $f(x)$;
(2) Determine the parity of $f(x)$ and provide a proof;
(3) When $a > 1$, find the range of $x$ that satisfies $f(x) > 0$.

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