
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 two fixed points $A(-1,0)$ and $B(1,0)$, a moving point $M$ satisfies $|AM|=4$. The perpendicular bisector of the segment $MB$ intersects with the segment $AM$ at point $N$. Let the trajectory of point $N$ be curve $C$.
(I) Find the equation of curve $C$.
(II) Suppose a moving line $l$ intersects with curve $C$ at points $P$ and $Q$, and $OP \perp OQ$ (where $O$ is the origin). Determine whether there exists a fixed circle $x^{2}+y^{2}=r^{2}(r > 0)$ such that it is always tangent to line $l$. Explain your reasoning.

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