
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 $f(x)=2\ln x+x^{2}-ax$.
(I) When $a=5$, find the monotonic intervals of $f(x)$;
(II) Let $A(x\_1,y\_1)$ and $B(x\_2,y\_2)$ be two distinct points on the curve $y=f(x)$. If the slope $k$ of the line $AB$ is always greater than 1, find the range of values for the real number $a$;
(III) Suppose the function $f(x)$ has two extreme points $x\_1$ and $x\_2$, with $x\_1 < x\_2$ and $x\_2 > e$. If $f(x\_1)-f(x\_2)\geqslant m$ always holds, find the range of values for the real number $m$.

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