
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
Given an arithmetic sequence $a\_n$ with the sum of its first $n$ terms being $S\_n$, if $(a\_2 - 1)^3 + 5(a\_2 - 1) = 1$ and $(a\_2010 - 1)^3 + 5(a\_2010 - 1) = -1$, find $a\_2 + a\_2010 = \_\_\_\_\_\_$ and $S\_2011 = \_\_\_\_\_\_$.

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