
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
Let  $n \leq 100$  be an integer. Hare puts real numbers in the cells of a  $100 \times 100$  table. By asking Hare one question, Wolf can find out the sum of all numbers of a square  $n \times n$ , or the sum of all numbers of a rectangle  $1 \times (n - 1)$  (or  $(n - 1) \times 1$ ). Find the greatest  $n{}$  such that, after several questions, Wolf can find the numbers in all cells, with guarantee.


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