
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
Calculate the sum $s = 1 + 2\omega + 3\omega^2 + 4\omega^3 + \cdots + (n+1) \omega^n$ where $\omega$ is a cube root of unity (i.e., $\omega^3 = 1$ and $\omega \neq 1$), and $n$ is a multiple of $3$.
**A)** $3m + 1$  
**B)** $m$  
**C)** $3m + 3$  
**D)** $3m$

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