
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
There are a total of 10040 numbers written on a blackboard, including 2006 of the number 1, 2007 of the number 2, 2008 of the number 3, 2009 of the number 4, and 2010 of the number 5. Each operation consists of erasing 4 different numbers and writing the 5th number (for example, erasing one 1, one 2, one 3, and one 4, and writing one 5; or erasing one 2, one 3, one 4, and one 5, and writing one 1, etc.). If after a finite number of operations, there are exactly two numbers left on the blackboard, what is the product of these two numbers?


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