
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 a moving circle $P$ that is internally tangent to the circle $E: (x+\sqrt{3})^2 + y^2 = 25$ and internally tangent to the circle $F: (x-\sqrt{3})^2 - y^2 = 1$, denote the trajectory of the center of circle $P$ as curve $C$.
(1) Find the equation of curve $C$;
(2) Line $l$ intersects curve $C$ at points $A$ and $B$, with point $M(1,1)$ being the midpoint of segment $AB$, find the equation of line $l$.

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