
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 inscribed in an isosceles right triangle is positioned such that one of its vertices touches the right-angle vertex of the triangle, and its opposite side is parallel to the hypotenuse of the triangle. If the side length of this inscribed square is $24\text{ cm}$, calculate the area of another square that can be inscribed in the same triangle by having one of its sides along the hypotenuse.

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