
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 summer festival day, $80$ people are wearing sunglasses, and $60$ people are wearing hats. Some attendees are wearing both sunglasses and hats. Unfortunately, if a person wearing a hat is chosen at random, the probability that they are also wearing sunglasses is $\frac{1}{3}$. If a person wearing sunglasses is chosen instead, what is the probability that they are also wearing a hat?
A) $\frac{1}{5}$
B) $\frac{2}{5}$
C) $\frac{1}{3}$
D) $\frac{1}{4}$

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