
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 $f(x)=e^{x}(x^{2}+2)$, $g(x)=\frac{x}{e}$  
$(1)$ Find the equation of the tangent line to the curve $y=f(x)$ at the point $(0,f(0))$.  
  
$(2)$ Find the maximum and minimum values of the function $h(x)=f(x)-g(x)$ in the interval $[-2,0]$.

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