
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 \( 5 \mathrm{~cm} \) by \( 5 \mathrm{~cm} \) pegboard and a \( 10 \mathrm{~cm} \) by \( 10 \mathrm{~cm} \) pegboard each have holes at the intersection of invisible horizontal and vertical lines that occur in \( 1 \mathrm{~cm} \) intervals from each edge. Pegs are placed into the holes on the two main diagonals of both pegboards. The \( 5 \mathrm{~cm} \) by \( 5 \mathrm{~cm} \) pegboard is shown; it has 16 holes. The 8 shaded holes have pegs, and the 8 unshaded holes do not. How many empty holes does the \( 10 \mathrm{~cm} \) by \( 10 \mathrm{~cm} \) pegboard have?


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