
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
Michael was walking in Marrakesh when he saw a tiling formed by tessellating the square tile. The tile has four lines of symmetry, and the length of each side is $8$ cm. The length of $XY$ is $2$ cm. The point $Z$ is such that $XZ$ is a straight line and $YZ$ is parallel to the sides of the square. What is the area of the central grey octagon?
A) $6 \text{ cm}^2$  
B) $7 \text{ cm}^2$  
C) $8 \text{ cm}^2$  
D) $9 \text{ cm}^2$  
E) $10 \text{ cm}^2$

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