
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 $f(x)=\ln x-ax-3$ $(a\neq 0)$  
$(1)$ Find the extreme values of the function $f(x)$;  
$(2)$ If for any $a\in[1,2]$, the function $g(x)=x^{3}+ \frac{x^{2}}{2}[m-2f′(x)]$ has an extremum in the interval $(a,3)$, find the range of the real number $m$.

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