
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 a base \( ABCD \) that is a rhombus with side length 2 and \( \angle ABC = 60^\circ \). Point \( E \) is the midpoint of \( AB \). \( PA \) is perpendicular to the plane \( ABCD \), and the sine of the angle between \( PC \) and the plane \( PAD \) is \( \frac{\sqrt{6}}{4} \).

(1) Find a point \( F \) on edge \( PD \) such that \( AF \parallel \) plane \( PEC \);

(2) Find the cosine of the dihedral angle between planes \( D-PE-A \).

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