
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 plane \( PAD \perp \) plane \( ABCD \), \(\triangle PAD\) is an equilateral triangle with side length 2, the base \( ABCD \) is a rhombus, and \(\angle BAD = 60^\circ\). Find the measure of the acute dihedral angle between planes \( PAD \) and \( PBC \).

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