
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
Given an integer  $n \geq 2$  determine the integral part of the number $ \sum_{k=1}^{n-1} \frac {1} {({1+\frac{1} {n}})	\dots ({1+\frac {k} {n})}}$  -  $\sum_{k=1}^{n-1} (1-\frac {1} {n})	\dots(1-\frac{k}{n})$ 

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