
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]


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Two concentric circles have radii \(3\) and \(5\). Two points are chosen such that one point is uniformly at random on the outer circle and another is fixed on the inner circle directly opposite to a random point on the outer circle. What is the probability that the chord formed by joining these two points intersects another smaller concentric circle of radius \(2\)?

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