
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
A convex quadrilateral EFGH has EF = 24, ∠E = 45°, and EF || GH. The lengths of the sides of the quadrilateral, in some order, form an arithmetic progression, and side EF is the side of maximum length. One of the other sides has length p. Find the sum of all possible values of p.

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