
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 $f(x)=x- \frac{2a}{x} -(a+2)\ln x$, where the real number $a\geqslant 0$.

$(1)$ If $a=0$, find the maximum and minimum values of the function $f(x)$ on the interval $x\in[1,3]$;

$(2)$ If $a > 0$, discuss the monotonicity of the function $f(x)$.

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