
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 6 by 6 grid, each of the 36 small squares measures 1.5 cm by 1.5 cm. The grid is fully shaded in grey. Six unshaded shapes are then added: one medium hexagon, four small circles placed symmetrically, and one larger circle in the center. The diameter of the small circles equals the side of a small square (1.5 cm), and the larger circle has a diameter of 3 cm; the side length of the hexagon equals 1.5 cm. Assume all circles and the hexagon are placed such that no parts of these shapes overlap. The area of the visible shaded region can be written in the form $A-B\pi - C\sqrt{3}$. What is the value $A+B+C$?

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