
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 side $AC$ of triangle $ABC$, points $M$ and $N$ are marked such that $M$ lies on segment $AN$. It is known that $AB = AN$ and $BC = MC$. The circumcircles of triangles $ABM$ and $CBN$ intersect at points $B$ and $K$. What is the angle $\angle AKC$ if $\angle ABC = 68^\circ$?

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