
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 that circle E passes through points M(-1, 0), N(0, 1), and P($$\frac{1}{2}$$, -$$\frac{\sqrt{3}}{2}$$).

1. Find the equation of circle E.
2. If a line is drawn through point C(2, 2) intersecting circle E at points A and B, find the equation of line AB.

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