
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
In the Cartesian coordinate system xOy, the circle M with equation $(x+1)^2+y^2=\frac{49}{4}$ has its center at M, and the circle N with equation $(x-1)^2+y^2=\frac{1}{4}$ has its center at N. A moving circle is internally tangent to circle M and externally tangent to circle N.  
(Ⅰ) Find the equation of the trajectory of the center P of the moving circle;  
(Ⅱ) A line l passing through the point (1, 0) intersects the curve P at points A and B. If $\overrightarrow{OA} \cdot \overrightarrow{OB} = -2$, find the equation of line l.

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