
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 \( (y_k) \) is defined by \( y_0 = 0 \), \( y_1 = 1 \), and
\[
y_{k + 2} = \frac{(n - 2) y_{k + 1} - (n - k - 1) y_k}{k + 1}
\]
for \( k \ge 0 \). Find \( y_0 + y_1 + y_2 + \dotsb \) as a function of \( n \).

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