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

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