
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 square pyramid with base  $ABCD$  and vertex  $E$  has eight edges of length 4.  A plane passes through the midpoints of  $\overline{AE}$ ,  $\overline{BC}$ , and  $\overline{CD}$ .  The plane's intersection with the pyramid has an area that can be expressed as  $\sqrt{p}$ .  Find  $p$ .

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