
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
Circles \(\omega_{1}\) and \(\omega_{2}\) with centers \(O_{1}\) and \(O_{2}\) respectively intersect at point \(B\). The extension of segment \(O_{2}B\) beyond point \(B\) intersects circle \(\omega_{1}\) at point \(K\), and the extension of segment \(O_{1}B\) beyond point \(B\) intersects circle \(\omega_{2}\) at point \(L\). A line passing through point \(B\) parallel to \(KL\) intersects circles \(\omega_{1}\) and \(\omega_{2}\) at points \(A\) and \(C\) respectively. Rays \(AK\) and \(CL\) intersect at point \(N\). Find the angle between lines \(O_{1}N\) and \(O_{2}B\).

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