
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 rectangular map has one corner folded such that its vertex falls somewhere along the side of the map. This folding results in three right triangles, the areas of which form an arithmetic progression. If the area of the smallest triangle is $3 \mathrm{~cm}^{2}$, what is the area of the largest triangle?

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