
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
Consider a sequence $\{a_n\}$ satisfying $a_4 = \frac{1}{8}$, and for any positive integer $n$, it satisfies $a_{n+2} - a_n \leq 3^n$ and $a_{n+4} - a_n \geq 10 \times 3^n$. Determine the value of $a_{2016}$.

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