
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 $f(x)=\ln x+x-\frac{1}{2}mx^2$.

(1) Find the extreme value points of the function $f(x)$ when $m=2$.

(2) Find the minimum integer value of $m$ such that the inequality $f(x)\leqslant mx-1$ always holds for $x$.

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