
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 positive integers greater than 1000 satisfy the following condition: the units digit of the sum of any two of the numbers is equal to the units digit of the third number. Find the number of possible values for the last three digits of the product of these three numbers.

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