
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
In triangle \( ABC \), the angle at vertex \( A \) is twice the angle at vertex \( C \). A tangent \( \ell \) to the circumcircle \( \Omega \) of triangle \( ABC \) is drawn through vertex \( B \). The distances from points \( A \) and \( C \) to this tangent are 5 and 12, respectively.
a) Find the distance from point \( A \) to line \( BC \).

b) Find the radius of the circumcircle \( \Omega \) and the length of side \( BC \).

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