
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 involving a population of women, the prevalence of three genetic markers, denoted by X, Y, and Z, is examined. The probability that a randomly selected woman has only one of these markers (and none of the others) is 0.15 for each marker. For any two of the three markers, the probability that a randomly selected woman has exactly these two markers (and not the third) is 0.18. The probability that a randomly selected woman has all three markers, given that she has X and Y, is $\frac{1}{4}$. Calculate the probability that a woman has none of the three markers given that she does not have marker X.

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