
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 a base $ABCD$ and vertex $E$ has all edges of length 5. A plane passes through the midpoints of $\overline{AE}$, $\overline{AB}$, and $\overline{CD}$. The intersection of this plane with the pyramid forms a polygon. Calculate the area of this intersection, which can be expressed as $\sqrt{q}$. Find the value of $q$.

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