
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
In a specific population, it is known that one in every 400 individuals is affected by a certain disease, which is asymptomatic. A particular test used to detect this disease always yields a positive result for those who have the disease. However, for those who do not have the disease, the test has a false positive rate of $3\%$. If a randomly selected individual from this population tests positive, let $p$ be the probability that this individual actually has the disease. Calculate $p$.
A) $\frac{1}{400}$
B) $\frac{1}{199}$
C) $\frac{100}{1297}$
D) $\frac{399}{400}$
E) $\frac{1297}{40000}$

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