
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
Define a sequence \( (y_k) \) for a positive integer \( m \) with initial conditions \( y_0 = 1 \), \( y_1 = m \), and for \( k \geq 0 \), the recurrence is given by
\[
y_{k+2} = \frac{(m + 1) y_{k+1} + (m - k) y_k}{k + 2}.
\]
Evaluate the sum \( y_0 + y_1 + y_2 + \dots \) as a function of \( m \).

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