
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 tetrahedral pyramid with vertices $A$, $B$, $C$, and $D$, where $AB = 6$, $BC = 4$, $CD = 5$, $AD = 4$, $BD = 5$, and $AC = 7$. A plane passes through the midpoint $M$ of $\overline{AD}$, vertex $B$, and the midpoint $N$ of $\overline{BC}$. The intersection of this plane with the pyramid forms a polygon. Find the area of this polygon.

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