
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 semicircle is inscribed in a right triangle such that the diameter lies on the hypotenuse, and the center divides the hypotenuse into segments of lengths 15 cm and 20 cm. Find the area of the triangle and the length of the inscribed semicircle.

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