
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
Let \( g(x) = x^2(1-x)^2 \). Compute the value of the sum
\[
g\left(\frac{1}{2023}\right) - g\left(\frac{2}{2023}\right) + g\left(\frac{3}{2023}\right) - g\left(\frac{4}{2023}\right) + \cdots + g\left(\frac{2021}{2023}\right) - g\left(\frac{2022}{2023}\right)
\]
A) \(\frac{1012^4}{2023^4}\)
B) \(\frac{1011^4}{2023^4}\)
C) \(\left(\frac{1012 \times 1011}{2023^2}\right)^2\)
D) \(\frac{1011 \times 1012}{2023^4}\)

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