
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, circle $A$ with radius 2 and circle $B$ with radius 1.5, are to be constructed with the following process: The center of circle $A$ is chosen uniformly and at random from the line segment joining $(0,0)$ to $(3,0)$. The center of circle $B$ is chosen uniformly and at random, and independently from the first choice, from the line segment joining $(1,2)$ to $(4,2)$. What is the probability that circles $A$ and $B$ intersect?
A) 0.90
B) 0.95
C) 0.96
D) 1.00

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