
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
Let \( A B C \) be a right triangle at \( C \), not isosceles, with legs \( b > a \).

(i) Find the side length of the square \( A X Y Z \) that circumscribes the triangle \( A B C \) (vertices \( B \) and \( C \) must be on different sides of the square).

(ii) Explain step by step how to construct the square \( A X Y Z \) using a straightedge and compass.

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