
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 E with a focal length of $2 \sqrt {5}$ and a right vertex. Point P is located at (0, $2 \sqrt {3}$). Line PA intersects ellipse E at point B, which is the midpoint of line segment PA.

1. Find the equation of ellipse E.
2. Suppose a line l passing through point P with a slope of k intersects ellipse E at points M and N, and $\overrightarrow {PN}=3 \overrightarrow {PM}$. Find the slope k of line l.

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