
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]


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The hypotenuse of a right triangle is \( c \), and one of the acute angles is \( \boldsymbol{\alpha} \). Two circles of the same radius are placed in the triangle, each touching one of the legs, the hypotenuse, and the other circle. Find the radii of these circles.

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