
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 fixed circle $A:(x+1)^{2}+y^{2}=16$, and a moving circle $M$ that passes through point $B(1,0)$ and is tangent to circle $A$.

(I) Find the trajectory equation of the moving circle's center $M$.

(II) If a line $l$ with slope $k (k \neq 0)$ intersects the trajectory of point $M$ at two distinct points $P$ and $Q$, and the area of the triangle formed by the perpendicular bisector of segment $PQ$ and the two coordinate axes is $\frac{1}{14}$, find the range of $k$.

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