
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 an ellipse $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a>b>0)$, the sum of the distances from a point P on the ellipse to the two foci $F_1$, $F_2$ is $2 \sqrt {2}$, and the eccentricity is $\frac{\sqrt{2}}{2}$.
(I) Find the equation of the ellipse;
(II) A line l passing through the right focus $F_2$ intersects the ellipse at points A and B. If a point $M(0, \frac{\sqrt{3}}{7})$ on the y-axis satisfies |MA|=|MB|, find the slope k of line l.

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