
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 population, 1 in 300 people is infected with a rare disease that shows no symptoms. A testing method is used to identify this disease. The test always returns a positive result if a person is infected. For individuals not infected, the false positive rate of the test is 3%. Calculate the probability $p$ that a person given a positive test result actually has the disease.
A) $\frac{1}{300}$
B) $\frac{100}{997}$
C) $\frac{3}{299}$
D) $\frac{299}{300}$

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