
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 the triangle \(ABC\), side \(AB\) is equal to \(\sqrt{11}\), and the angle at vertex \(A\) is twice the angle at vertex \(C\). A tangent \(\ell\) to the circumcircle \(\Omega\) of the triangle \(ABC\) is drawn through vertex \(B\). The distances from points \(A\) and \(C\) to this tangent are in the ratio \(9:25\).

a) Find the ratio of the distances from point \(A\) to the lines \(\ell\) and \(BC\).

b) Find the distance from point \(C\) to the line \(\ell\) and the radius of the circumcircle \(\Omega\).

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