
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
Given a semicircle. Consider the triangles whose one side contains the diameter of the semicircle and whose other two sides touch the semicircle. Which of these triangles has the smallest area?

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