
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 $n$ be a positive integer. The sequence $(x_k)$ is defined by $x_0 = 1,$ $x_1 = n,$ and
\[x_{k + 2} = \frac{(n - 1) x_{k + 1} - (n - k) n x_k}{k + 1}\]for $k \ge 0.$ Find $x_0 + x_1 + x_2 + \dotsb$ as a function of $n.$

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