
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
Consider several black and white chips placed in a circle. Two players take turns executing the following operations: the first player removes all black chips that have a white neighbor (on at least one side), and the second player removes all white chips that have a black neighbor. They continue doing this until all chips remaining are of the same color.

a) Initially, there were 40 chips. Could it happen that after each player has made two turns, there is only one chip remaining on the circle?

b) Suppose there were initially 1000 chips. What is the minimum number of turns required before only one chip remains on the circle?

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