
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
The side length of a regular hexagon is 12 cm. The shaded region is defined by an equilateral triangle whose vertices are every second vertex of the hexagon. Find the number of square centimeters in the area of the non-shaded region. Express your answer in simplest radical form.

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