
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 extension of the diameter \(AB\) of a circle, a segment \(BC\) equal in length to the diameter is laid off. A line passing through point \(C\) is tangent to the circle at point \(M\). Find the area of triangle \(ACM\) if the radius of the circle is \(R\).

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