
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 regular hexagon with side length 4, there are six alternating semicircles along its sides such that the diameters of three of them equal the side of the hexagon, and the other three have diamimeters equal to half the side length. Calculate the area of the region inside the hexagon but outside all the semicircles.

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