
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 $f(x)=\frac{1}{2}x^{2}-2a\ln x+(a-2)x$, where $a\in R$.
(1) If the function $f(x)$ is monotonically increasing on $(2,+\infty)$, find the range of the real number $a$;
(2) Discuss the minimum value $g(a)$ of $f(x)$ on $[2,e]$.

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