
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 right triangle with sides 6, 8, and 10, where 10 is the hypotenuse, and a square inscribed in this triangle with one vertex at the right-angle vertex, find the ratio of the side length of this square to the side length of another square inscribed in a similar right triangle with the same side lengths, where one side of this square lies on the hypotenuse.

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