
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 $f\left(x\right)=x^{2}-3x+\ln x$.  
$(1)$ Find the extreme values of the function $f\left(x\right)$;  
$(2)$ For any $x_{1}$, $x_{2}\in \left[1,2\right]$, when $x_{1} \lt x_{2}$, the inequality $x_{1}x_{2}(f(x_{1})-f(x_{2}))-m(x_{1}-x_{2}) \gt 0$ always holds. Find the range of real number $m$.

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