
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
An ellipse C is defined by the equation $$\frac {x^{2}}{a^{2}}$$+ $$\frac {y^{2}}{b^{2}}$$\=1, where a>b>0. The eccentricity of the ellipse is $$\frac { \sqrt {2}}{2}$$. B<sub>1</sub> and B<sub>2</sub> are the endpoints of the minor axis of the ellipse, and |B<sub>1</sub>B<sub>2</sub>|=6. Point M moves on the ellipse and does not coincide with B<sub>1</sub> or B<sub>2</sub>. Point N is such that NB<sub>1</sub> is perpendicular to MB<sub>1</sub>, and NB<sub>2</sub> is perpendicular to MB<sub>2</sub>.

(I) Find the equation of ellipse C.
(II) Find the maximum area of the quadrilateral MB<sub>2</sub>NB<sub>1</sub>.

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