
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: $1$, $1$, $2$, $3$, $5$, $8$, $13$, $21$, $34$, $55$, $89$, $144$, $233$, $(\ldots)$, that is, $F(1)=F(2)=1$, $F(n)=F(n-1)+F(n-2)$ $(n \geqslant 3, n \in \mathbb{N}^{*})$. This sequence has a wide range of applications in modern physics, quasicrystal structures, chemistry, etc. If the remainder of this sequence divided by $3$ forms a new sequence $\{b_{n}\}$, then $b_{2017}=$ \_\_\_\_\_\_.

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