
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
Three circles, each of radius 2, are to be drawn such that the center of circle $A$ is chosen uniformly at random from the line segment joining $(0,0)$ and $(4,0)$. Circle $B$'s center is chosen from $(0,2)$ to $(4,2)$, and Circle $C$'s center is chosen from $(0,-2)$ to $(4,-2)$. What is the probability that all three circles intersect at least at one point?
A) 0.5
B) 0.375
C) 0.25
D) 0.125
E) 0.0625

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