
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
Evaluate the expression $S = i^{n+1} + i^{-n}$, where $i = \sqrt{-1}$ and $n$ is an integer. Determine the total number of possible distinct values for $S$.
- **A)** 8
- **B)** 2
- **C)** 1
- **D)** 4
- **E)** More than 8

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