
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

Given the numerical sequence:

\[x_{0}=\frac{1}{n}, \quad  x_{k}=\frac{1}{n-k}\left(x_{0}+x_{1}+\ldots+x_{k-1}\right), \quad k=1,2, \ldots, n-1.\]

Find \(S_{n}=x_{0}+x_{1}+\ldots+x_{n-1}\) for \(n=2021\).

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