
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
A line cuts off a triangle \( A K N \) from a regular hexagon \( A B C D E F \) such that \( A K + A N = A B \). Find the sum of the angles at which the segment \( K N \) is viewed from the vertices of the hexagon (\( \angle K A N + \angle K B N + \angle K C N + \angle K D N + \angle K E N + \angle K F N \)).

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