
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 of diameter 3 sits atop a semicircle of diameter 4. Calculate the area of the lune formed by the area inside the smaller semicircle and outside the larger semicircle. Express your answer in terms of \(\pi\) and in simplest radical form.

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