
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

On the side \(AC\) of triangle \(ABC\), points \(M\) and \(N\) are marked (with \(M\) lying on segment \(AN\)). It is known that \(AB = AN\) and \(BC = MC\). The circumcircles of triangles \(ABM\) and \(CBN\) intersect at points \(B\) and \(K\). How many degrees is the angle \(AKC\) if \(\angle ABC = 68^\circ\)?

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