
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
Consider the parabolas $y = (x + 2)^2$ and $x + 2 = (y - 1)^2$. These curves intersect at several points. Determine if these intersection points lie on a circle and find $r^2$, the square of the circle's radius.

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