
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 $\{a\_n\}$, $a\_1=-2014$. Let $S\_n$ denote the sum of the first $n$ terms. If $\frac{S\_2012}{2012} - \frac{S\_10}{10} = 2002$, find the value of $S\_2016$.

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