
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 $A(0,2)$ and $B(-1,1)$, and the 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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