
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 \( a_{0}, a_{1}, \cdots, a_{n} \) satisfies:
\[ 
a_{0}=\sqrt{3}, \quad a_{n+1}=[a_{n}]+\frac{1}{\{a_{n}\}} 
\]
where \( [x] \) denotes the greatest integer less than or equal to the real number \( x \), and \( \{x\}=x-[x] \). Find the value of \( a_{2016} \).

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