
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 E: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$$ (where $a>b>0$) has an eccentricity of $$\frac { \sqrt {3}}{2}$$. A perpendicular line to the x-axis passing through the left focus intersects the ellipse at points A and B, and $|AB|=1$. (1) Find the equation of ellipse E; (2) Suppose P and Q are two points on ellipse E, with P in the first quadrant and Q in the second quadrant, and $OP \perp OQ$, where O is the origin. When P and Q move, is there a fixed circle O such that line PQ is always tangent to circle O? If it exists, find the equation of circle O; if not, explain why.

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