
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 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 lines $AL$ and $KL$.

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