
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 that the derivative of the function $f(x)$, denoted as $f'(x)$, satisfies the inequality $(x+x\ln x)f'(x)>f(x)$ for all $x\in(1,+\infty)$.
(1) Determine the monotonicity of the function $g(x)=\frac{f(x)}{1+\ln x}$ on the interval $(1,+\infty)$, and explain your reasoning.
(2) If $f(x)=e^x+mx$, find the range of values for $m$.

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