
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 \(y_0 = 1\), \(y_1 = m\), and for \(k \geq 0\),
\[
y_{k+2} = \frac{m \cdot y_{k+1} - (m+k) \cdot y_k}{k+1}.
\]
Find the sum \(y_0 + y_1 + y_2 + \dots\) as a function of \(m\).

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