
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 one of every 200 people in a certain population has a particular disease, which displays no symptoms. A diagnostic test is available for screening for this disease. For a person who has this disease, the test always turns out positive. For a person who does not have the disease, however, there is a $5\%$ false positive rate--in other words, for such people, $95\%$ of the time the test will turn out negative, but $5\%$ of the time the test will turn out positive and will incorrectly indicate that the person has the disease. Let $p$ be the probability that a person who is chosen at random from this population and gets a positive test result actually has the disease.
A) $\frac{10}{219}$
B) $\frac{20}{219}$
C) $\frac{30}{219}$
D) $\frac{40}{219}$
E) $\frac{50}{219}$

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