
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 $10 \times 10$ square, numbers from 1 to 100 are arranged: in the first row from 1 to 10 left to right, in the second row from 11 to 20 left to right, and so on. Andrei plans to cut the square into $1 \times 2$ dominoes, calculate the product of the numbers in each domino, and sum the resulting 50 numbers. He aims to obtain the smallest possible sum. How should he cut the square?

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