
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 E: $$\frac {x^{2}}{a^{2}}$$ + $$\frac {y^{2}}{b^{2}}$$ = 1 (a > b > 0) with its right focus F (1, 0), and point B (0, b) satisfying |FB| = 2.
(I) Find the equation of ellipse E;
(II) A line l passes through point F and intersects ellipse E at points M and N. If the ratio of the areas of △BFM and △BFN is 2, find the equation of line l.

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