
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

Consider a $10 \times 10$ grid $A$ where each cell contains an integer. Let $s_i$ be the sum of the numbers in the $i$-th row and $t_j$ be the sum of the numbers in the $j$-th column for $i, j = 1, 2, \ldots, 10$. We then create a new $10 \times 10$ grid $B$ where the value in the cell at the $i$-th row and $j$-th column is the minimum of $s_i$ and $t_j$. We know that it is possible to number the cells in grid $B$ from 1 to 100 such that the value in the $k$-th cell is not greater than $k$. Determine the maximum possible sum of all the numbers in grid $A$.

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