
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 $\{a_{n}\}$, the sum of its first $n$ terms is $S_{n}$. If $a_{1}=-2010$, and $\frac{S_{2009}}{2009} - \frac{S_{2007}}{2007} = 2$, find the value of $S_{2011}$.

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