
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
The area of a right triangle is given by \(\frac{2}{\frac{2}{r}} 2\), where \(r\) is the radius of the circle that touches one leg and the extensions of the other leg and the hypotenuse. Find the sides of the triangle.

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