
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
Given the sequence $\left\{a_{n}\right\}$ defined by:
$$
a_{0}=\sqrt{3}, \quad a_{n+1}=\left[a_{n}\right]+\frac{1}{\left\{a_{n}\right\}},
$$

where $[x]$ denotes the greatest integer less than or equal to the real number $x$, and $\{x\}=x-[x]$. Determine the value of $a_{2019}$.

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