
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 the sequence 2010, 2011, 1, -2010, -2011, ..., the characteristic of this sequence is that starting from the second term, each term is equal to the sum of its previous and next terms. Then, the sum of the first 2012 terms of this sequence, $S_{2012}$, is equal to ______.

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