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

(1) Find the domain of the function $F(x)=f(x)-g(x)$;

(2) Determine the even or odd property of $F(x)=f(x)-g(x)$ and explain the reason;

(3) When $a > 1$, find the set of values of $x$ that make $F(x) > 0$.

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