
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 $f(x)=mx-\ln x-3 (m\in R)$.
(1) Discuss the number of extreme points of the function $f(x)$ in its domain;
(2) If the function $f(x)$ takes an extreme value at $x=1$, and there exists $x\in(0,+\infty)$ such that $f(x)\leqslant nx-4$ has a solution, find the range of values of the real number $n$;
(3) When $0 < a < b < 4$ and $b\neq e$, compare $\frac{1-\ln a}{1-\ln b}$ with $\frac{a}{b}$.

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