
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
In the arithmetic sequence $\left\{a_{n}\right\}$ where $a_{1}=-2011$, the sum of the first n terms is represented by $S_{n}$. Given that $\frac{S_{2012}}{2012} - \frac{S_{2011}}{2011} = 1$, determine the value of $S_{2013}$.

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