
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 a sequence $\{a_n\}$ that satisfies $a_{n+1}=\begin{cases}2a_{n} & (0\leq a_{n}\leq \frac{1}{2}) \\ 2a_{n}-1 & (\frac{1}{2}\leq a_{n} < 1)\end{cases}$, if $a_{1}=\frac{4}{5}$, determine the value of $a_{2017}$.

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