
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
Gauss is a famous German mathematician, known as the "Prince of Mathematics". There are 110 achievements named after "Gauss". Let $x\in \mathbb{R}$, $[x]$ denotes the greatest integer less than or equal to $x$, and $\{x\}=x-[x]$ represents the non-negative fractional part of $x$. Then $y=[x]$ is called the Gauss function. Given a sequence $\{a_n\}$ satisfies: $a_1=\sqrt{3}, a_{n+1}=[a_n]+\frac{1}{\{a_n\}}, n\in \mathbb{N}^*$, then $a_{2017}=$ __________.

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