
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: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{4}=1$$ (where $a>2$), a point P on the ellipse has a total distance of 6 from its two foci, F<sub>1</sub> (left) and F<sub>2</sub> (right).  
(1) Find the eccentricity of ellipse C;  
(2) If PF<sub>2</sub> is perpendicular to the x-axis, and the projection of P on the y-axis is point Q, find the coordinates of point Q.

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