
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
On a board in a laboratory, two numbers are written. Each day, the senior researcher, Petrov Ivanovich, erases both numbers from the board and writes their arithmetic mean and 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 written on the board in the evening of the 2016th day.

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