
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 the rhombus \(A B C D\), the angle at vertex \(A\) is \(60^{\circ}\). Point \(N\) divides side \(A B\) in the ratio \(A N: B N = 2: 1\). Find the tangent of angle \(D N C\).

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