
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
Compute
\[
\sum_{n = 2}^\infty \frac{6n^3 - 2n^2 - 2n + 2}{n^6 - n^5 + n^4 - n^3 + n^2 - n + 1}.
\]

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