
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
A sequence of real numbers  $\{a_n\}_{n = 1}^\infty (n=1,2,...)$  has the following property:
\begin{align*}
6a_n+5a_{n-2}=20+11a_{n-1}\  (\text{for }n\geq3).
\end{align*}
The first two elements are  $a_1=0, a_2=1$ . Find the integer closest to  $a_{2011}$ .

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