
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

We place 2004 two-colored chips forming a circle: white on one side and black on the other. A move consists of choosing a black chip and flipping three chips: the chosen one, the one on its right, and the one on its left. Suppose that initially, there is only one chip with the black side facing up. Will it be possible, by repeating the described move, to make all the chips have the white side facing up? What if we had 2003 chips, among which exactly one has the black side facing up at the beginning?

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