
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
In a triangle, the sides are in the ratio 2:3:4. A semicircle is inscribed with its diameter lying on the longest side. Find the ratio of the area of the semicircle to the area of the triangle.

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