
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
Two circles, each of radius 2, are constructed as follows: The center of circle A is chosen uniformly at random from the line segment joining (0,0) and (2,0). The center of circle B is chosen uniformly at random from the line segment joining (0,2) to (2,2), with the additional condition that the center of B must lie above or on the line y = 1. Calculate the probability that circles A and B intersect.

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