
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
Consider an isosceles right triangle $\triangle DEF$ with $DE = EF$. A square is inscribed inside this triangle such that one vertex of the square is at the right-angle vertex of the triangle, and two of its sides are coincident with the two legs of the triangle. If the area of this square is found to be $784 \text{cm}^2$, determine the area (in $\text{cm}^2$) of another square inscribed in the same $\triangle DEF$ where its sides are parallel to the hypotenuse and one of its vertices is also at the right-angle vertex.

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