
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 health study of a population of women, the probability that a randomly selected woman has only one of three risk factors (denoted as D, E, and F) is 0.08 for each factor. The probability that a randomly selected woman has exactly two of these risk factors (but not the third) is 0.12 for each pair. The probability that a randomly selected woman has all three risk factors, given that she has D and E, is $\frac{1}{4}$. The probability that a woman has none of the three risk factors given that she does not have risk factor D needs to be calculated and expressed as $\frac{r}{s}$, where $r$ and $s$ are relatively prime positive integers. Find $r+s$.

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