
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
Nation $X$ has $p\%$ of the world's population and $q\%$ of the world's total wealth, while Nation $Y$ has $r\%$ of the population and $s\%$ of the wealth. Each nation distributes its wealth equally among its citizens. If Nation $X$ has an income inequality index which reduces its actual wealth distribution by half, calculate the ratio of the wealth of a citizen of Nation $X$ to that of a citizen of Nation $Y$.
A) $\frac{qr}{ps}$
B) $\frac{qs}{pr}$
C) $\frac{0.5qr}{ps}$
D) $\frac{2ps}{qr}$
E) $\frac{pr}{qs}$

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