
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 sequence \( \left\{a_{n}\right\} \) is defined as follows: \( a_{0}=\sqrt{3} \), and \( a_{n+1}=\left[a_{n}\right]+\frac{1}{\left\{a_{n}\right\}} \) (where \( \left[a_{n}\right] \) and \( \left\{a_{n}\right\} \) represent the integer part and fractional part of the real number \( a_{n} \), respectively). Find \( a_{2019} \).

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