
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
The Italian mathematician Leonardo Fibonacci introduced the "Fibonacci sequence" using rabbit reproduction as an example: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ..., where $F(1)=F(2)=1$, and $F(n)=F(n-1)+F(n-2)$ ($n\geq3$, $n\in\mathbb{N}^*$). This sequence has a wide range of applications in modern physics, quasicrystal structures, chemistry, etc. If a new sequence $\{b_n\}$ is formed by the remainder after dividing this sequence by 3, find $b_{2017}$.

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