
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 $h(x) = g(x) - a(x^3 + x^2)$ ($a > 0$).

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