
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 his name "Gauss". For $x\in R$, let $[x]$ represent the largest integer not greater than $x$, and let $\{x\}=x-[x]$ 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: $a_{1}=\sqrt{3}$, $a_{n+1}=[a_{n}]+\frac{1}{\{a_{n}\}}$, $(n∈N^{*})$, then $a_{2019}=$\_\_\_\_\_\_\_\_.

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