
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
Given a rectangular parallelepiped \(A B C D A_1 B_1 C_1 D_1\), where \(A B = 4\), \(A D = 2\), \(A A_1 = 6\). Point \(N\) is the midpoint of edge \(C D\), point \(M\) is located on edge \(C C_1\), with the ratio \(C_1 M : C M = 1 : 2\), and point \(K\) is the intersection of the diagonals of face \(A A_1 D_1 D\). Find the angle between lines \(KM\) and \(A_1 N\).

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