
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
Three natural numbers are such that the last digit of the sum of any two of them is the last digit of the third number. The product of these three numbers was written on the board, and then everything except the last three digits of this product was erased. What three digits could remain on the board? Find all possible answers.

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