
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 $f\left(x\right)=\log _{a}(3-x)+\log _{a}(x+1)$, where $a \gt 0$ and $a\neq 1$. <br/>$(1)$ Find the domain and the equation of the axis of symmetry of the graph of $f\left(x\right)$; <br/>$(2)$ If the maximum value of $f\left(x\right)$ is $2$, find the value of $a$.

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