
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 $a\neq 1)$, define $h(x)=f(x)-g(x)$.

1. Determine the domain of $h(x)$.
2. Identify the odd or even property of $h(x)$, and provide the rationale.
3. If $a=\log_{3}27+\log_{\frac{1}{2}}2$, find the set of $x$ that satisfies $f(x) > 1$.

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