
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
Give the closed form (as a function of $k$ and $n$) for the sum of the following series:

$$
\binom{k}{1} \sum_{i=1}^{n} i+\binom{k}{2} \sum_{i=1}^{n} i^{2}+\ldots+\binom{k}{k-1} \sum_{i=1}^{n} i^{k-1}
$$

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