
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 radius of the arc of the sector is \(R\), and the central angle \(AOB\) is \(\alpha\). A line is drawn through the midpoint \(C\) of the radius \(OA\), parallel to the radius \(OB\), and intersects the arc \(AB\) at point \(D\). Find the area of triangle \(OCD\).

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