
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 $f\left(x\right)=(x^{2}+mx+1)e^{x}$.  
$(1)$ If $m=0$, find the equation of the tangent line to $f\left(x\right)$ at $\left(0,f\left(0\right)\right)$;  
$(2)$ If the function $f\left(x\right)$ has exactly one local minimum point in $\left(-1,1\right)$, find the range of real number $m$;  
$(3)$ If for any $x\in \left(0,\pi \right)$, $f\left(x\right) \gt e^{x}(x^{2}\cos x+1)$ always holds, find the range of real number $m$.

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