
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 functions $f\left(x\right)=2x^{2}e^{x}$ and $g\left(x\right)=ax+2a\ln x\left(a\in R\right)$.  
$(1)$ Find the monotonic intervals and extreme values of the function $f\left(x\right)$;  
$(2)$ If the function $h\left(x\right)=f\left(x\right)-g\left(x\right)$ has $2$ zeros, find the range of real number $a$.

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