
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 C: $$\frac {x^{2}}{a^{2}} + \frac {y^{2}}{b^{2}} = 1$$ ($a > b > 0$) with eccentricity $$\frac {\sqrt {2}}{2}$$, and vertices A($a$, 0), B(0, $b$), the distance from the center O to the line AB is $$\frac {2}{ \sqrt {3}}$$.  
(1) Find the equation of ellipse C;  
(2) Suppose there is a moving point P on ellipse C satisfying: $$\overrightarrow {OP} = \lambda \overrightarrow {OM} + 2\mu \overrightarrow {ON}$$, where M, N are points on ellipse C, and the product of the slopes of lines OM and ON is -$$\frac {1}{2}$$. If Q($\lambda$, $\mu$) is a moving point, and E<sub>1</sub>($- \frac { \sqrt {3}}{2}$, 0), E<sub>2</sub>($\frac { \sqrt {3}}{2}$, 0) are two fixed points, find the value of |QE<sub>1</sub>| + |QE<sub>2</sub>|.

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