
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 \(A O\) of a circle with center \(O\), a point \(M\) is chosen. Points \(B\) and \(C\) are chosen on the circle on one side of \(A O\) such that \(\angle A M B = \angle O M C = \alpha\). Find the length of \(B C\) if the radius of the circle is 12 and \(\cos \alpha = \frac{3}{4}\).

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