
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 two circles with radii 2 and 1.5, where circle A's center is chosen uniformly at random on the line segment joining (0,0) and (3,0), and circle B's center is chosen uniformly at random, independently from the first choice, on the line segment joining (0,2) to (3,2), find the probability that the circles A and B intersect.

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