
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
In a line, 2020 white stones and one black stone are arranged. A possible operation is as follows: choose a black stone that is not at the border and change the color of its neighboring stones. Find all the possible initial positions for the black stone such that it is possible to color all the stones black with a finite number of operations.

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