
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 a circle O: x²+y²=r² and an ellipse C: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a＞b＞0)$$, the short semi-axis length of the ellipse C is equal to the radius of the circle O. A line passing through the right focus of C is tangent to the circle O at point $$D( \frac {1}{2}, \frac { \sqrt {3}}{2})$$.

1. Find the equation of the ellipse C.
2. If a moving line l is tangent to the circle O and intersects C at points A and B, find the maximum distance from point O to the perpendicular bisector of chord AB.

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