
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 quadrilateral pyramid \(PABCD\), the lateral face \(P A D\) is an equilateral triangle and is perpendicular to the base \(ABCD\). The base \(ABCD\) is a rhombus with side length 2, and \(\angle B A D = 60^\circ\). Let \(N\) be the midpoint of \(P B\), and the cross-section \(DAN\) intersects \(P C\) at \(M\). Find the dihedral angle between the planes \(P-AD-M\).

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