
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
Points \( A, B, C \) lie on a circle \(\omega\) such that \( BC \) is a diameter. \( AB \) is extended past \( B \) to point \( B' \) and \( AC \) is extended past \( C \) to point \( C' \) such that line \( B'C' \) is parallel to \( BC \) and tangent to \(\omega\) at point \( D \). If \( B'D = 4 \) and \( C'D = 6 \), compute \( BC \).

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