
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 $f(x)=a(x+1)^2$ and $g(x)=xe^x$.
1. If the tangent line of $g(x)$ passes through $(-4,0)$, find the equation of the tangent line.
2. Discuss the number of intersection points between the graphs of $f(x)$ and $g(x)$.

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