
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 with the equation $\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$ (where $0>b>0$) with its right vertex at point A and upper vertex at point B. The focal length of the ellipse is $2 \sqrt {5}$, and the slope of line AB is $- \frac {2}{3}$.

1. Find the standard equation of the ellipse.
2. Let line $l: y=kx$ (where $k<0$) intersect the ellipse at points M and N, with point M in the second quadrant. Line $l$ intersects the extension of line AB at point P. If the area of triangle BNP is three times the area of triangle BMN, find the value of $k$.

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