
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 right-angled triangle with an acute angle $\alpha$ is inscribed in a circle of radius $r$ such that the hypotenuse is a chord of the circle, and the vertex of the right angle lies on the diameter parallel to the hypotenuse. Find the area of the triangle.

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