
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 square with side length \( x \) is inscribed in a right triangle with sides of length \( 6 \), \( 8 \), and \( 10 \) so that one side of the square lies along the leg of length \( 6 \). Another square with side length \( y \) is inscribed in the same right triangle with another side along the leg of length \( 8 \). What is \( \frac{x}{y} \)?
A) \(\frac{8}{9}\)
B) \(\frac{35}{37}\)
C) \(\frac{9}{8}\)
D) \(\frac{7}{8}\)
E) \(\frac{4}{3}\)

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