
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 quadrilateral pyramid \(P-ABCD\) with \(PB \perp AD\). The lateral face \(PAD\) is an equilateral triangle with a side length of 2, and the base \(ABCD\) is a rhombus. The dihedral angle between the lateral face \(PAD\) and the base \(ABCD\) is \(120^\circ\).

(I) Find the distance from point \(P\) to the plane \(ABCD\).
(II) Find the dihedral angle between the faces \(APB\) and \(CPB\).

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