
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
In an isosceles right triangle, a square is inscribed such that its side length is half the length of the triangle's hypotenuse. If the area of this square is $400 \text{cm}^2$, calculate the area of a square inscribed in the same triangle such that its diagonal equals the length of one leg of the triangle.

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