
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 \(\ell\) is drawn from vertex \(B\) to the circumcircle \(\Omega\) of triangle \(ABC\). The distances from points \(A\) and \(C\) to this tangent are 4 and 9, respectively.
a) Find the distance from point \(A\) to the line \(BC\).

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

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