
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 right triangle, the shorter side is $x$, and the longer leg is $y$. The hypotenuse of the triangle is $z$. A perpendicular drawn from the right angle vertex to the hypotenuse divides it into two segments: $u$ adjacent to $x$ and $v$ adjacent to $y$. Given the ratio of the legs is $x:y = 3:4$, calculate the ratio $u:v$.
A) $\frac{3}{5}$
B) $\frac{4}{9}$
C) $\frac{9}{16}$
D) $\frac{16}{25}$
E) $\frac{5}{8}$

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