
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
Consider two concentric circles where the inner circle has radius $3$ and the outer circle has a radius $5$. Two points on the outer circle are chosen independently and uniformly at random. Determine the probability that the chord joining these two points intersects the inner circle.
**A)** $\frac{\tan^{-1}(\frac{1}{2})}{\pi}$
**B)** $\frac{\tan^{-1}(\frac{3}{4})}{\pi}$
**C)** $\frac{\tan^{-1}(1)}{\pi}$
**D)** $\frac{\tan^{-1}(\frac{2}{3})}{\pi}$

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