
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
Liam is investigating the prevalence of three types of dietary deficiencies, denoted by D, E, and F, within a group of students. For each of the three deficiencies, the probability that a randomly selected student has only this deficiency (and not the others) is 0.07. For any two of the three deficiencies, the probability that a randomly selected student has exactly these two deficiencies (but not the third) is 0.05. The probability that a randomly selected student has all three deficiencies, given that he has D and E is $\frac{1}{4}$. The probability that a student has none of the three deficiencies given that he does not have deficiency D is $\frac{r}{s}$, where $r$ and $s$ are relatively prime positive integers. Find $r+s$.

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