
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
Let $x=m$ and $x=n$ be the two extreme points of the function $f(x)=2\ln{x}+x^2-2(a+3)x$, where $m<n$, $a\in\mathbb{R}$.
(1) Find the range of $f(m)+f(n)$;
(2) If $a\geq \sqrt {e}+ \frac{1}{ \sqrt {e}}-3$, find the maximum value of $f(n)-f(m)$.

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