
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

...

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Let  $ n$  and  $ k$  be positive integers. Please, find an explicit formula for
\[ \sum y_1y_2 \dots y_k,\]
where the summation runs through all  $ k\minus{}$ tuples positive integers  $ (y_1,y_2,\dots,y_k)$  satisfying  $ y_1\plus{}y_2\plus{}\dots\plus{}y_k\equal{}n$ .

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