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

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