
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 $f(x)=(\frac{1}{2}{{x}^{2}}+ax)\ln x-\frac{1}{4}{{x}^{2}}-ax$, where $a\in R$.

(1) If $a=0$, find the equation of the tangent line to the curve $y=f(x)$ at $x=e$;

(2) If $a < 0$, find the extreme values of the function $f(x)$;

(3) If $f(x) > 0$ always holds, find the range of values for the real number $a$.

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