
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
Let the function $f(x)=\log_{2}\frac{x+1}{x-1}+\log_{2}(x-1)+\log_{2}(p-x)$.  
$(1)$ Find the domain of the function;  
$(2)$ When $p > 3$, does $f(x)$ have a maximum and minimum value? If it exists, please write it down; if not, please explain why.

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