
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
Consider the sum $s = 1 - 2i + 3i^2 - 4i^3 + 5i^4 - 6i^5 + \cdots + (-1)^n (n+1) i^n$ where $i = \sqrt{-1}$ and $n$ is a multiple of $3$. Compute $s$ for such $n$.

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