
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 $10 \times 10$ table, a natural number is written. Then, each cell is painted if the number written in that cell is less than one of its neighbors but greater than another neighbor. (Two numbers are considered neighbors if they are in cells sharing a common side.) As a result, only two cells remain unpainted, and neither of these cells is in a corner. What is the minimum possible sum of the numbers in these two cells?

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