
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 $f(x)=2\ln x+x^2-mx,(m\in R)$.

(1) If $f(x)$ is monotonically increasing in its domain, find the range of values for the real number $m$.

(2) If $5 < m < \frac{17}{2}$, and $f(x)$ has two extreme points $(x_1,x_2)(x_1 < x_2)$, find the range of values for $f(x_1)-f(x_2)$.

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