
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
On the segment \( AB \) with length \( 2R \), a semicircle is constructed with \( AB \) as the diameter, and a chord \( CD \) is drawn parallel to \( AB \). Find the volume of the solid formed by rotating the triangle \( ACD \) around the diameter \( AB \), given that the inscribed angle subtended by the arc \( AC \) is \( \alpha \) \((AC < AD)\).

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