
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
Given a square with side length $x$ inscribed in a right triangle with side lengths 3, 4, and 5, such that one vertex of the square coincides with the right-angled vertex of the triangle. Another square with side length $y$ is also inscribed in the same right triangle, with one side of the square on the hypotenuse of the triangle. Find the value of $\frac{x}{y}$.

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