
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 table \( A \) of size \( 10 \times 10 \), some numbers are written. Let the sum of all numbers in the first row be denoted as \( s_{1} \), in the second row as \( s_{2} \), and so on. Similarly, the sum of the numbers in the first column is denoted as \( t_{1} \), in the second column as \( t_{2} \), and so on.

A new table \( B \) of size \( 10 \times 10 \) is constructed such that in the first cell of the first row is written the smallest of the numbers \( s_{1} \) and \( t_{1} \), in the third cell of the fifth row is written the smallest of the numbers \( s_{5} \) and \( t_{3} \), and so on for the whole table. It turns out that it is possible to number the cells of table \( B \) with numbers from 1 to 100 such that in the cell with number \( k \) there will be a number less than or equal to \( k \). What is the maximum value that the sum of all the numbers in table \( A \) can take under these conditions?

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