
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 the board. Each day, senior research associate Petya erases both numbers and writes their arithmetic mean and their harmonic mean instead. On the morning of the first day, the numbers 1 and 2 were written on the board. Determine the product of the numbers written on the board at the end of the 1999th day.

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