
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
Find \(\sum_{k=0}^n \frac{(-1)^k \binom{n}{k}}{k^3 + 9k^2 + 26k + 24}\), where \(\binom{n}{k} = \frac{n!}{k!(n-k)!}\).

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