
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 $x^{3011} = 1$ and $x \neq 1$. Compute the sum
\[
\frac{x^3}{x-1} + \frac{x^9}{x^3-1} + \frac{x^{15}}{x^5-1} + \dots + \frac{x^{9033}}{x^{3011}-1}.
\]

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