
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 that passes through the origin and the point (2,0), and its center C lies on the line y=2x.
(1) Find the equation of circle C;
(2) Draw tangents PA and PB to circle C through point P(-2,2), and find the equations of lines PA and PB.

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