
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
Lucy is asked to choose \( p, q, r, \) and \( s \) to be the numbers 1, 2, 3, and 4, in some order, so as to make the value of \( \frac{p}{q} + \frac{r}{s} \) as small as possible. What is the smallest value Lucy can achieve in this way?

A) \( \frac{7}{12} \)

B) \( \frac{2}{3} \)

C) \( \frac{3}{4} \)

D) \( \frac{5}{6} \)

E) \( \frac{11}{12} \)

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