
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
The squares of an $8 \times 8$ chessboard are numbered somehow with the numbers from 1 to 64. Let's call the "distance" between two neighboring squares the absolute difference between the numbers on them. (Two squares are considered neighboring if they share a common vertex.) What is the greatest number which can occur as the distance between neighboring squares on the chessboard, regardless of how the chessboard is numbered?

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