
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 $f(x)=\log_{a}(1-2x)-\log_{a}(1+2x)$ where $a > 0$ and $a \neq 1$:
1. Determine the domain of $f(x)$.
2. Determine the symmetry (odd or even) of $f(x)$ and provide a proof.
3. Find the range of $x$ for which $f(x) > 0$.

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