
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 $f(x)=\ln x+\frac{1}{2}x^2-ax$, where $a\in \mathbb{R}$, it has two extreme points at $x=x_1$ and $x=x_2$, with $x_1 < x_2$.

(I) When $a=3$, find the extreme values of the function $f(x)$.

(II) If $x_2\geqslant ex_1$ ($e$ is the base of the natural logarithm), find the maximum value of $f(x_2)-f(x_1)$.

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