
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 a sequence $\{a_n\}$ that satisfies the recurrence $a_n = \frac{a_{n-1}}{a_{n-2}}$ for $n \in \mathbb{N}^{*}$ and $n \geq 3$, with $a_1=2$ and $a_2=\frac{1}{3}$, find the value of $a_{2016}$.

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