
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
An invisible tank is on a  $100 \times 100 $  table. A cannon can fire at any  $k$  cells of the board after that the tank will move to one of the adjacent cells (by side). Then the progress is repeated. Find the smallest value of  $k$  such that the cannon can definitely shoot the tank after some time. 

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