
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 the recursion 
$$
a_{n+1} = 
\begin{cases} 
2a_{n} & \text{if } 0 \leq a_{n} \leq \frac{1}{2},\\
2a_{n} - 1 & \text{if } \frac{1}{2} \leq a_{n} < 1,
\end{cases}
$$
where $a_1 = \frac{6}{7}$. Calculate the value of $a_{2017}$.

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