
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
The numbers 1, 2, ..., 2016 are written on a board. You are allowed to erase any two numbers and write their arithmetic mean instead. How must you proceed so that the number 1000 remains on the board?

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