
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 one side of $AO$, points $B$ and $C$ are chosen on the circle such that $\angle AMB = \angle OMC = \alpha$. Find the length of $BC$ if the radius of the circle is 21 and $\sin \alpha = \frac{\sqrt{40}}{7}$.

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