
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
In the polar coordinate system, with O as the pole, the polar coordinates of the center of circle C, which has a radius of 2, are (2, $$\frac{\pi}{3}$$).
(1) Find the polar equation of circle C;
(2) In the Cartesian coordinate system with the pole O as the origin and the polar axis as the positive x-axis, the parametric equation of line l is $$\begin{cases} x=1+\frac{1}{2}t \\ y=-2+\frac{\sqrt{3}}{2}t \end{cases}$$ (with t as the parameter). Line l intersects circle C at points A and B. Given a fixed point M (1, -2), find the product |MA|•|MB|.

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