
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
Let  $n$  be an integer. We consider  $s (n)$ , the sum of the  $2001$  powers of  $n$  with the exponents  $0$  to  $2000$ . So  $s (n) = \sum_{k=0}^{2000}n ^k$  . What is the unit digit of  $s (n)$  in the decimal system?

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