
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
In a right triangle \(ABC\) with \(\angle A = 60^{\circ}\), point \(N\) is marked on the hypotenuse \(AB\), and point \(K\) is the midpoint of segment \(CN\). It is given that \(AK = AC\). The medians of triangle \(BCN\) intersect at point \(M\). Find the angle between lines \(AM\) and \(CN\).

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