
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 250 people in a certain population has a particular disease, which shows no symptoms. A blood test is used for screening this disease. For a person who has this disease, the test result is always positive. For a person who does not have the disease, there is a $3\%$ false positive rate. Let $q$ be the probability that a person who is randomly selected from this population and tests positive for the disease, actually has the disease.
A) $\frac{1}{12}$
B) $\frac{1}{11}$
C) $\frac{1}{10}$
D) $\frac{1}{9}$

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