
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 $f(x)=\frac{1}{2}{x}^{2}-(a+1)x+a\mathrm{ln}x$, where $a>0$.

(I) When $a=2$, find the monotonic intervals of the function $f(x)$;

(II) If $x=2$ is the extremum point of the function $f(x)$, find the extreme value of the function $f(x)$ in the interval $[1,3]$.

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