
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 $xOy$, given are circle $O_{1}$: $(x+1)^{2}+y^{2}=1$ and circle $O_{2}$: $(x-1)^{2}+y^{2}=9$. A moving circle $P$ is externally tangent to circle $O_{1}$ and internally tangent to circle $O_{2}$.
   
(Ⅰ) Find the equation of the trajectory $E$ of the center of circle $P$;
   
(Ⅱ) Through point $A(-2,0)$, draw two perpendicular lines $l_{1}$ and $l_{2}$, intersecting curve $E$ at points $M$ and $N$ respectively. Let the slope of $l_{1}$ be $k(k > 0)$, and the area of $\triangle AMN$ be $S$, find the range of $\dfrac{S}{k}$.

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