
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
On a beach, $120$ people are wearing sunglasses, and $84$ people are wearing caps. Some people are wearing both sunglasses and caps. Additionally, there are $60$ people wearing hats, some of whom also wear at least one of the other two accessories. If one of the people wearing a cap is selected at random, the probability that this person is also wearing sunglasses is $\frac{3}{7}$. Find the probability that a person selected at random wearing sunglasses is also wearing a cap.

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