
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
Henry is studying the prevalence of three health risk factors, denoted by X, Y, and Z, within a population of women. For each of the three factors, the probability that a randomly selected woman in the population has only this risk factor (and none of the others) is 0.05. For any two of the three factors, the probability that a randomly selected woman has exactly these two risk factors (but not the third) is 0.07. The probability that a randomly selected woman has all three risk factors, given that she has X and Y is $\frac{1}{4}$. The probability that a woman does not have any of the three risk factors given that she does not have risk factor X is to be determined as $\frac{p}{q}$, 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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