
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
On a diamond-shaped checkerboard formed by an 8x8 grid, what is the probability that a randomly chosen unit square does not touch a vertex of the diamond? Assume a diamond shape results from rotating the square checkerboard 45 degrees (so vertices will be the center of former edge squares), and a square touches a vertex if it shares that vertex.
A) $\frac{1}{4}$
B) $\frac{1}{2}$
C) $\frac{3}{4}$
D) $\frac{7}{8}$
E) $\frac{15}{16}$

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