
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 $\{a_n\}$ such that:
$$
a_{n+1}=
\begin{cases}
2a_n & \text{if } 0 \leq a_n \leq 1,\\
a_n - 1 & \text{if } a_n > 1,
\end{cases}
$$
and $a_1 = \frac{6}{7}$. Find the value of $a_{2017}$.

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