
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
The circles \(\omega_{1}\) and \(\omega_{2}\) with centers \(O_{1}\) and \(O_{2}\) respectively intersect at point \(A\). Segment \(O_{2}A\) intersects circle \(\omega_{1}\) at point \(K\) again, and segment \(O_{1}A\) intersects circle \(\omega_{2}\) at point \(L\) again. A line through point \(A\) parallel to \(KL\) intersects circles \(\omega_{1}\) and \(\omega_{2}\) at points \(C\) and \(D\) respectively again. Segments \(CK\) and \(DL\) intersect at point \(N\). Find the angle between lines \(O_{1}A\) and \(O_{2}N\).

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