
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
The base of a pyramid with vertex \( P \) is a quadrilateral \( ABCD \), where the sum of angles \( A \) and \( D \) is five times the sum of angles \( B \) and \( C \). Find the angle between the planes of the faces \( PAB \) and \( PCD \) if they are both perpendicular to the base.

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