
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 particular study of health conditions in a village, researchers are analyzing three health risk factors, denoted by P, Q, and R, within a group of 500 people. For each of these three factors, the probability that a randomly selected individual in the population has only this risk factor (and no others) is 0.08. For any two of the three factors, the probability that a randomly selected individual has exactly these two risk factors (but not the third) is 0.18. The probability that a randomly selected individual has all three risk factors is 0.05. The probability that an individual does not have any of the three risk factors given that he does not have risk factor P is represented by $\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Calculate $p+q$.

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