
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
Circle \(\omega_{1}\) with center \(O\) intersects with circle \(\omega_{2}\) at points \(K\) and \(L\). Circle \(\omega_{2}\) passes through point \(O\). A line through point \(O\) intersects circle \(\omega_{2}\) again at point \(A\). Segment \(OA\) intersects circle \(\omega_{1}\) at point \(B\). Find the ratio of the distances from point \(B\) to the lines \(AL\) and \(KL\).

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