
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 regular hexagon has a side length of 4, and six semicircles are drawn inside it such that their diameters coincide with the sides of the hexagon. Additionally, there is a smaller concentric regular hexagon inside the larger hexagon, each of its sides tangent to one of the semicircles. Find the area of the region inside the larger hexagon but outside all of the semicircles and the smaller hexagon.

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