
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
Determine the smallest integer  $j$  such that it is possible to fill the fields of the table  $10\times 10$  with numbers from  $1$  to  $100$  so that every  $10$  consecutive numbers lie in some of the  $j\times j$  squares of the table.

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