
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, one with radius 2 and the other with radius 3, are to be placed as follows. The center of the circle with radius 2 is to be chosen uniformly and at random from the line segment joining (0,0) to (5,0). The center of the other circle is placed at (3,2). Determine the probability that the two circles intersect.

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