
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 $h(x)$, determine the parity of $h(x)$, and explain the reason;  
$(2)$ 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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