
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 four edges from the vertex of length 5 and four edges of the base of length 6. A plane passes through the midpoints of $\overline{AE}$, $\overline{BD}$, and $\overline{CD}$. Compute the area of the triangle formed by the intersection of this plane with the pyramid.

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