
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
Petya inscribed two squares in a right triangle with sides 3, 4, and 5. One vertex of the first square coincides with the right-angle vertex of the triangle, while one side of the second square lies on the hypotenuse. Petya found the side lengths of each square, expressed their ratio as an irreducible fraction, and found the sum of the numerator and denominator of that fraction. What number did Petya get? (Recall that a quadrilateral is called inscribed in a triangle if all its vertices are located on the sides or at the vertices of the triangle.)

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