
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
Catherine is studying the prevalence of three health conditions, denoted by X, Y, and Z, in a group of women. For each of the three conditions, the probability that a randomly selected woman has only that condition (and not the others) is 0.12. For any two of the conditions, the probability that a randomly selected woman has exactly those two conditions (but not the third) is 0.16. The probability that a randomly selected woman has all three conditions, given she has conditions X and Y, is $\frac{1}{4}$. Calculate the number of women with no health conditions if the group consists of 200 women.

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