
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 center of circle $M$ is given by the equation $(x+1)^{2}+y^{2}= \frac {49}{4}$, and the center of circle $N$ is given by the equation $(x-1)^{2}+y^{2}= \frac {1}{4}$. 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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