
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 circle $A: x^{2}+y^{2}+2x-15=0$ and a fixed point $B(1,0)$, $M$ is any point on circle $A$, and the perpendicular bisector of segment $MB$ intersects $MA$ at point $N$. Let the trajectory of point $N$ be $C$.
- (I) Find the equation of $C$;
- (II) If the line $y=k(x-1)$ intersects curve $C$ at points $P$ and $Q$, is there a fixed point $R$ on the x-axis such that $\angle ORP = \angle ORQ$ holds as $k$ varies? If it exists, find the coordinates of point $R$; if not, explain why.

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