
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
Two numbers are written on a board. Every day, the senior researcher, Petya, erases both numbers and writes their arithmetic mean and their harmonic mean in their place. On the morning of the first day, the numbers 1 and 2 were written on the board. Find the product of the numbers on the board in the evening of the 1999th day.

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