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

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