
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
Given a rhombus with side length \( a \) and acute angle \( \alpha \).

Find the radius of the circle that passes through two adjacent vertices of the rhombus and is tangent to the opposite side of the rhombus or its extension.

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