
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 C passes through the intersection points of the line x+y+2=0 and the circle x²+y²=4, and the center of circle C is on the line 2x-y-3=0, find the equation of circle C.

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