
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]


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Gauss is a famous German mathematician, known as the "Prince of Mathematics". There are 110 achievements named after "Gauss". Let $x\in\mathbb{R}$, use $[x]$ to represent the largest integer not exceeding $x$, and use $\{x\}=x-[x]$ to represent the non-negative fractional part of $x$. Then, $y=[x]$ is called the Gauss function. It is known that the 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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