
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 $10 \times 10$ grid filled with the integers from 1 to 100: the first row contains 1 to 10 from left to right; the second row contains 11 to 20 from left to right; and so on. Andre tries to divide the entire grid into $1 \times 2$ rectangles, then calculates the product of the two numbers in each rectangle, and sums up the 50 products obtained. How should he divide the grid so that the resultant sum is as small as possible?

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