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

1. Find the range of $f(m)+f(n)$;
2. If $a\geqslant \sqrt{e}+\frac{1}{\sqrt{e}}-2$, find the maximum value of $f(n)-f(m)$ (Note: $e$ is the base of the natural logarithm).

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