
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 \( O \), point \( M \) is chosen. On the same side of \( A O \) on the circumference, points \( B \) and \( C \) are chosen such that \( \angle A M B = \angle O M C = \alpha \). Find the length \( B C \), given that the radius of the circle is 15 and \( \cos \alpha = \frac{3}{5} \).

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