
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 a sequence $\{a_n\}$, where $S_n$ is the sum of its first $n$ terms. If $a_1=1$, $a_2=2$, and $a_na_{n+1}a_{n+2}=a_n+a_{n+1}+a_{n+2}$ with $a_{n+1}a_{n+2} \neq 1$, then find $S_{2011}$.

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