
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 $f(x)=(ax-1)\ln x+ \frac{x^{2}}{2}$.
(I) If $a=2$, find the equation of the tangent line $l$ to the curve $y=f(x)$ at the point $(1,f(1))$;
(II) Let the function $g(x)=f'(x)$ have two extreme points $x_{1}$, $x_{2}$, where $x_{1}∈(0,e)$, find the minimum value of $g(x_{1})-g(x_{2})$.

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