
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
As shown in the diagram, a triangle \(ABC\) is folded along the segment \(DE\) to form a heptagon \(ADED\). If the area ratio between the heptagon and the original triangle is \(5:7\), and the overlapping area after folding is \(8 \text{ cm}^2\), find the area of the original triangle \(ABC\).

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