
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 $f\left(x\right)=\log _{a}(1+bx)-\log _{a}(1-x)$ where $(a \gt 0$ and $a\neq 1, b \gt 0)$ is an odd function.<br/>$(1)$ Find the domain of $f\left(x\right)$;<br/>$(2)$ Find the solution set of the inequality $f\left(x\right) \gt 0$ in terms of $x$.

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