
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 $f(x)=x^{2}+x-\ln x-1$.  
$(1)$ Find the extreme points of the function $f(x)$;  
$(2)$ If $g(x)=f(x)-m\frac{e^{2x}}{x}$ is monotonically decreasing on $\left[1,+\infty \right)$, find the range of the real number $m$.

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