
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 $\{a_n\}$, it is known that $a_1 = -2$, $a_2 = -1$, $a_3 = 1$. If for any positive integer $n$, $a_na_{n+1}a_{n+2}a_{n+3} = a_n + a_{n+1} + a_{n+2} + a_{n+3}$, and $a_{n+1}a_{n+2}a_{n+3} \neq 1$, then calculate 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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