
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 the sum of its first $n$ terms is $S\_n$, $a\_1=-1$, $a\_2=2$, and $S_{n+1}=3S\_n-2S_{n-1}-a_{n-1}+2$ ($n\geqslant 2$), find $a_{2016}$.

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