
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 at the top of a semicircle of diameter 4. The upper semicircle slightly overlaps with the lower semicircle. Determine the area of the lune formed, expressed in terms of $\pi$ and in simplest form. Both semicircles share a common chord.

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