
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
A right triangle has sides 5, 12, and 13, with 13 being the hypotenuse. A square with side length $x$ is inscribed in this triangle so that one side of the square lies along one of the legs of the triangle (length 12). Another square with side length $y$ is inscribed in the same triangle so that one side of the square lies along the hypotenuse. What is the ratio $\frac{x}{y}$?
A) $\frac{5}{13}$
B) $\frac{17}{18}$
C) $\frac{11}{12}$
D) $\frac{12}{13}$
E) $\frac{13}{12}$

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