
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 $f\left(x\right)=\log _{a}(3-x)-\log _{a}(3+x)$ ($a \gt 0$, and $a\neq 1$).  
$(1)$ Determine the parity of the function and explain the reason.  
$(2)$ If $f\left(1\right)=-1$, find the range of $f\left(x\right)$ when $x\in \left[-1,1\right]$.

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