
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 two circles, circle M with equation $(x+1)^2 + y^2 = 1$, and circle N with equation $(x-1)^2 + y^2 = 9$. A moving circle P is tangent to circle M on the outside and tangent to circle N on the inside. The trajectory of the center of circle P is the curve C.
1. Find the equation of curve C.
2. A line l passing through the point $(-4,0)$ is tangent to circle M and intersects curve C at points A and B. Find the length of segment $|AB|$.

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