
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
In each unit square of square  $100*100$  write any natural number. Called rectangle with sides parallel sides of square  $good$  if sum of number inside rectangle divided by  $17$ . We can painted all unit squares in  $good$  rectangle. One unit square cannot painted twice or more.
Find maximum  $d$  for which we can guaranteed paint at least  $d$  points.

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