
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 circle C_1: $((x+2)^{2}+(y-3)^{2}=5)$ intersects with circle C_2 at points A(0,2), B(-1,1), and quadrilateral C_1AC_2B is a parallelogram, determine the equation of circle C_2.

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