
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. Define the sequence $(y_k)$ by $y_0 = 1$, $y_1 = m$ and for $k \geq 0$,
\[ y_{k+2} = \frac{(m-2)y_{k+1} - (m-k-1)y_k}{k+2}. \]
Find the sum $y_0 + y_1 + y_2 + \ldots + y_m$.

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