
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
The incidence rate of a certain disease among residents is $1\%$. A general survey and test are now being conducted, and medical research shows that there may be errors in the test results. It is known that among those who have the disease, $99\%$ test positive, while among those who do not have the disease, $1\%$ test positive. Given a person's test result is positive, calculate the probability that he really has the disease.

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