
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 $a_{n+1} = \begin{cases} 2a_n, & \text{if } a_n > 1 \ (0 \leqslant a_n \leqslant 1) \\ a_n - 1, & \text{if } a_n \leqslant 1 \end{cases}$, and $a_1 = \frac{6}{7}$. Find $a_{2017}$.

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