
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 $\{F_n\}$, which satisfies: $F_1 = F_2 = 1$, $F_{n+2} = F_{n+1} + F_n$ ($n \in \mathbb{N}^*$), and $r_n$ is the remainder when $F_n$ is divided by 3, find the value of $r_{2011}$.

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