
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 $f(x)=\ln x - mx + 2$.  
$(1)$ Find the extreme values of $f(x)$.  
$(2)$ If $f(x)$ has $2$ zeros in the interval $[\frac{1}{{e}^{2}}, e]$, find the range of values for $m$.

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