
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

a) Divide the interval \([0,1]\) into black and white segments such that for any polynomial \(p(x)\) of degree not higher than two, the sum of the increments of \(p(x)\) over all black segments is equal to the sum of the increments of \(p(x)\) over all white segments. 

(The increment of a polynomial \(p\) over the interval \((a, b)\) is defined as the number \(p(b) - p(a)\).)

b) Is it possible to perform a similar operation for all polynomials of degree not higher than 1995?

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