
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 10-foot by 12-foot floor is tiled with hexagonal tiles. Each hexagonal tile has a side length of 1 foot, and each tile is designed with six white sectors, each forming a $60^\circ$ segment of a circle with radius 1/2 foot located at the corners. The remaining area of each tile is shaded.
Calculate how many square feet of the floor are shaded.

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