
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 of radius 2 are to be constructed as follows. The center of circle $A$ is chosen uniformly and at random from the line segment joining $(0,0)$ and $(3,0)$. The center of circle $B$ is chosen uniformly and at random, and independently of the first choice, from the line segment joining $(0,2)$ to $(3,2)$. What is the probability that circles $A$ and $B$ intersect?
A) $\frac{7\sqrt{3} - 4}{9}$
B) $\frac{6\sqrt{3} - 4}{9}$
C) $\frac{9\sqrt{3} - 5}{9}$
D) $\frac{8\sqrt{3} - 4}{9}$

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