
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 \( f(x) = x^2(1-x)^2 \). Determine the value of the sum 
\( f \left(\frac{1}{2021} \right)-f  \left(\frac{2}{2021} \right)+f \left(\frac{3}{2021} \right)-f \left(\frac{4}{2021} \right)+\cdots + f \left(\frac{2019}{2021} \right) - f \left(\frac{2020}{2021} \right) \).

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