
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 study of a certain population, three health risk factors A, B, and C are being considered. The probability that a randomly selected individual in the population has only one specific risk factor (and not the others) is 0.08. The probability that a person has exactly two of these factors (but not the third) is 0.12. If a randomly selected person has both B and C, the probability that they also have A is $\frac{3}{5}$. Determine the probability that a person has none of the risk factors given they do not have risk factor B, expressed as $\frac{p}{q}$ where $p$ and $q$ are coprime positive integers. Find the value of $p + q$.

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