
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 table  $110\times 110$  is given, we define the distance between two cells  $A$  and  $B$  as the least quantity of moves to move a chess king from the cell  $A$  to cell  $B$ . We marked  $n$  cells on the table  $110\times 110$  such that the distance between any two cells is not equal to  $15$ . Determine the greatest value of  $n$ .

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