
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 specific genetic disorder, which is asymptomatic. A genetic test used to detect this disorder is perfectly sensitive (if you have the disorder, it always tests positive). However, for those without the disorder, there is a $5\%$ false positive rate. Let $p$ be the probability that a person chosen at random from this population who tests positive actually has the disorder. What is $p$ closest to?
A) $\frac{1}{200}$
B) $\frac{20}{219}$
C) $\frac{1}{10}$
D) $\frac{1}{50}$
E) $\frac{1}{20}$

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