
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
A point $N(1,0)$ is fixed inside the circle $M: (x+1)^2 + y^2 = 16$. $P$ is any point on the circle. The perpendicular bisector of the segment $(NP)$ intersects the radius $(MP)$ at point $Q$.

(I) What is the curve of the trajectory of point $Q$ as point $P$ moves on the circle? And derive its trajectory equation.

(II) A line $l$ passing through the point $G(0,1)$ intersects the curve $E$ at points $A$ and $B$. The point $D$ is the symmetric point of $A$ with respect to the origin $O$. Calculate the maximum area $S$ of the triangle $ABD$.

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