
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
Suppose that in a certain population, one out of every 300 individuals has an asymptomatic disease. A diagnostic test is used to detect this disease. The test is completely sensitive (positive in every case where disease is present). If the individual does not have the disease, there is a 1% chance that the test will still incorrectly return a positive result. Let $p$ be the probability that a randomly selected individual with a positive test result actually has the disease. What is $p$ closest to?
A) 0.100
B) 0.234
C) 0.251
D) 0.333
E) 0.299

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