
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 the ellipse $C$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a > b > 0)$ with eccentricity $e= \frac{1}{2}$, and point $P( \frac{2 \sqrt{6}}{3},1)$ on the ellipse $C$.

(I) Find the equation of the ellipse $C$;

(II) If the line $y=kx+b(k\neq 0)$ intersects the ellipse $C$ at two distinct points, and the perpendicular bisector of line segment $AB$ passes through the fixed point $M( \frac{1}{6},0)$, find the range of values for the real number $k$.

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