
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 \( f(x) = x^{2}(1-x)^{2} \). Evaluate the sum $\displaystyle f \left(\frac{1}{2023} \right)-f  \left(\frac{2}{2023} \right)+f \left(\frac{3}{2023} \right)-f \left(\frac{4}{2023} \right)+\cdots + f \left(\frac{2021}{2023} \right) - f \left(\frac{2022}{2023} \right)$.

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