
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 \(a_{0}, a_{1}, a_{2}, \cdots, a_{n}\) satisfies \(a_{0}=\sqrt{3}\), \(a_{n+1}=\left\lfloor a_{n}\right\rfloor + \frac{1}{\left\{a_{n}\right\}}\), where \(\left\lfloor a_{n}\right\rfloor\) and \(\left\{a_{n}\right\}\) represent the integer part and fractional part of \(a_{n}\), respectively. Find \(a_{2016}\).

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