
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
In rhombus \(ABCD\) and in triangle \(ABC\), both of which contain its larger diagonal, circles are inscribed. Find the ratio of the radii of these circles if the acute angle of the rhombus is \(\alpha\).

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