
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 \( f(x) = x^{2}(1-x)^{2} \). What is the sum
\[ f\left(\frac{2}{2021}\right) - f\left(\frac{3}{2021}\right) + f\left(\frac{4}{2021}\right) - f\left(\frac{5}{2021}\right) + \cdots + f\left(\frac{2020}{2021}\right)? \]
A) 0
B) \(\frac{1}{2021^4}\)
C) \(\frac{2020^2}{2021^4}\)
D) \(\frac{2022^2}{2021^4}\)
E) 1

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