
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
Carlos is researching the prevalence of four health risk factors, denoted by A, B, C, and D, within a community. For each of the four factors, the probability that a randomly selected individual in the community has only this risk factor (and none of the others) is 0.05. For each pair of the four factors, the probability that a randomly selected individual has exactly these two risk factors (and not the others) is 0.07. The probability that a randomly selected individual with risk factors A and B has all four risk factors A, B, C, and D is $\frac{1}{4}$. The probability that an individual has none of the four risk factors, given that they do not have risk factor A, is required to be found in simplest form $\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.

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