
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 radius \( AO \) of a circle with center \( O \), a point \( M \) is chosen. On the same side of \( AO \) on the circle, points \( B \) and \( C \) are chosen so that \( \angle AMB = \angle OMC = \alpha \). Find the length of \( BC \), given that the radius of the circle is 12 and \( \sin \alpha = \frac{\sqrt{11}}{6} \).

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