
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 $100 \times 100$ table, a natural number is written. It turns out that each number is either greater than all of its neighbors or less than all of its neighbors. (Two numbers are called neighbors if they are in cells that share a common side.) What is the smallest value that the sum of all the numbers can take?

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