
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
Derek fills a square  $10$  by  $10$  grid with  $50$   $1$ s and  $50$   $2$ s. He takes the product of the numbers in each of the  $10$  rows. He takes the product of the numbers in each of the  $10$  columns. He then sums these  $20$  products up to get an integer  $N.$  Find the minimum possible value of  $N.$ 

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