
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 $\{a\_n\}$ satisfies $a_{n+1}= \begin{cases} 2a_{n},0 \leqslant a_{n} < \dfrac {1}{2} \\ 2a_{n}-1, \dfrac {1}{2} \leqslant a_{n} < 1 \end{cases}$, and $a_{1}= \dfrac {6}{7}$. Find the value of $a_{2016}$.

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