
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 cell of a 200 x 200 square grid, a real number not exceeding 1 in absolute value was written. It turned out that the sum of all the numbers is zero. What is the smallest value of \( S \) for which it can be asserted that the sum of the numbers in some row or some column is necessarily not exceeding \( S \) in absolute value?

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