
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: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$$ (where $a>b>0$) has an eccentricity of $$e= \frac { \sqrt {3}}{2}$$, and the distance from the origin to the line passing through points A ($-a$, 0) and B (0, $b$) is $$\frac {4 \sqrt {5}}{5}$$.
(1) Find the equation of ellipse C;
(2) Let the moving line $l$ intersect with two fixed lines $l_1$: $x-2y=0$ and $l_2$: $x+2y=0$ at points P and Q, respectively. If line $l$ always has exactly one common point with ellipse C, investigate whether the area of $\triangle OPQ$ has a minimum value. If it exists, find this minimum value; if not, explain why.

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