
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 $g(x)=e^{x}(x+1)$.  
$(1)$ Find the equation of the tangent line to the function $g(x)$ at the point $(0,1)$.  
$(2)$ Let $x > 0$, discuss the number of zeros of the function $h(x)=g(x)-a(x^{3}+x^{2})$ where $a > 0$.

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