
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 functions $f(x) = \log_a(1+x)$ and $g(x) = \log_a(1-x)$, where $(a>0$ and $a \neq 1)$. Let $h(x) = f(x) - g(x)$.
(1) Find the domain of the function $h(x)$;
(2) Determine the parity of $h(x)$ and provide an explanation;
(3) If $f(3) = 2$, find the set of $x$ for which $h(x)>0$ holds.

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