
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 a \(7 \times 7\) table, some cells are black while the remaining ones are white. In each white cell, the total number of black cells located with it in the same row or column is written; nothing is written in the black cells. What is the maximum possible sum of the numbers in the entire table?

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