
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
Mara is researching the incidence of three lifestyle risk factors, denoted by X, Y, and Z, in a group of 200 women. For each of these three factors, the probability that a randomly selected woman has only this specific risk factor (and none of the others) is 0.05. The probability that a randomly selected woman has exactly two of these 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 has none of the three risk factors given that she does not have risk factor X is $\frac{s}{t}$, where $s$ and $t$ are relatively prime positive integers. Find $s+t$.

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