
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 $f(x)=x(\ln x-1)$,
(I) Find the equation of the tangent line to the curve $y=f(x)$ at the point $(1,f(1))$;
(II) If the function $g(x)=f(x)-\frac{a}{2}x^{2}$ has two extreme points $x_{1}$, $x_{2}$, compare $\frac{1}{\ln x_{1}}+\frac{1}{\ln x_{2}}$ with $2ae$.

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