
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
Two distinct squares of the  $8\times8$  chessboard  $C$  are said to be adjacent if they have a vertex or side in common.
Also,  $g$  is called a  $C$ -gap if for every numbering of the squares of  $C$  with all the integers  $1, 2, \ldots, 64$  there exist twoadjacent squares whose numbers differ by at least  $g$ . Determine the largest  $C$ -gap  $g$ .

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