
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 $$\frac { \sqrt {3}}{2}$$, and the point (-$$\sqrt {3}$$, $$\frac {1}{2}$$) lies on the ellipse C.  
(1) Find the equation of ellipse C;  
(2) Line l intersects ellipse C at points P and Q, with the midpoint of segment PQ being H, and O being the origin with OH=1. Find the maximum area of triangle POQ.

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