
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 contains eight semicircles, where each semicircle's diameter coincides with each side of the hexagon. Find the area of the region inside the hexagon but outside all of the semicircles.

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