
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 $f(x)=\ln x$.
$(1)$ If the function $g(x)=f(x)-ax+ \frac {1}{2}x^{2}$ has two extreme points, find the range of the real number $a$;
$(2)$ If the equation $f(x)=m(x+1)$, $(m\in \mathbb{Z})$ has a real solution, find the maximum value of the integer $m$.

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