
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 with sides of length $6$, $8$, and $10$, a square is inscribed such that one vertex of the square coincides with the right-angle vertex of the triangle. Another square is inscribed in the same triangle so that its one side lies along the hypotenuse of the triangle. What is the ratio of the side length of the first square to that of the second square?
A) \( \frac{35}{37} \)
B) \( \frac{70}{37} \)
C) \( \frac{888}{1680} \)
D) \( \frac{37}{70} \)

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