
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 the sequence $\{a_n\}$ satisfies $a_{n+1} = \begin{cases} 2a_{n}, & 0 \leq a_{n} < \frac{1}{2} \\ 2a_{n}-1, & \frac{1}{2} \leq a_{n} < 1 \end{cases}$, if $a_1 = \frac{6}{7}$, calculate the value of $a_{2016}$.

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