
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 $x$ be a complex number such that $x^{1001}=1$ and $x \neq 1$. Compute the sum
\[\frac{x^3}{x-1} + \frac{x^6}{x^2-1} + \frac{x^9}{x^3-1} + \dots + \frac{x^{3003}}{x^{1000}-1}.\]

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