
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 $P-ABCD$, the face $PAD$ is an equilateral triangle and is perpendicular to the base $ABCD$, which is a rhombus with sides of length 2 and $\angle BAD = 60^\circ$. Let $N$ be the midpoint of $PB$ and the cross-section $DAN$ intersects $PC$ at $M$. Find the dihedral angle $P-AD-M$.

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