
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 that the quadrilateral pyramid P-ABCD has a rectangular base ABCD and PA is perpendicular to the base ABCD. Points E and F are the midpoints of edges PC and PD, respectively. Determine which of the following statements are correct:
① Edge AB is perpendicular to the line containing PD;
② Plane PBC is perpendicular to plane ABCD;
③ The area of triangle PCD is greater than the area of triangle PAB;
④ Line AE and line BF are skew lines.
Write down the numbers of all correct conclusions.

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