
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 2009, 2010, 1, -2009, -2010, ..., the characteristic of this sequence is that starting from the second term, each term is equal to the sum of its adjacent terms. Determine the sum of the first 2010 terms of this sequence, S_{2010}.

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