
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 with side length $2$ has an isosceles right triangle placed at each of its corners, with the legs of each triangle lying along the sides of the square. The sum of the areas of the four isosceles right triangles is equal to the area of the square. Determine the length of the hypotenuse of one of the isosceles right triangles.

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