
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 C: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a＞b＞0)$$ with eccentricity e= $$\frac {1}{2}$$, and passing through the point ($$\sqrt {3}$$, $$\frac { \sqrt {3}}{2}$$)  
(I) Find the equation of ellipse C;  
(II) Two lines l<sub>1</sub> and l<sub>2</sub> passing through A(-a, 0) and perpendicular to each other intersect ellipse C at another two points P and Q, respectively. Does the line PQ pass through a fixed point? If so, find this fixed point; otherwise, explain why.

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