
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
Find the largest natural number \( N \) such that, for any arrangement of distinct natural numbers from 1 to 400 in the cells of a \( 20 \times 20 \) square table, there will be two numbers in the same row or column whose difference is at least \( N \).

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