
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 \( ABC \) with hypotenuse \( BC \). Around it, describe a semicircle with endpoints \( B \) and \( C \); then draw inside the triangle \( ABC \) an arc of a circle tangent to side \( AB \) at point \( B \) and side \( AC \) at point \( C \). The area of the region enclosed between this arc and the described semicircle is equal to the area of the original triangle. Why?

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