
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 a given circle, let \( AB \) be a side of an inscribed square. Extend \( AB \) to \( C \) such that \( BC = AB \). If \( C \) is connected to the center \( O \) of the circle and \( OC \) intersects the circle at \( D \), then \( CD \) is equal to twice the side length of a regular decagon inscribable in the circle.

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