
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 $a_{n+1} = \begin{cases} 2a_{n}, & 0\leq a_{n}\leq \frac {1}{2} \\ 2a_{n}-1, & \frac {1}{2}<a_{n}<1 \end{cases}$, with $a_1 = \frac {3}{5}$. Let $S_n$ be the sum of the first $n$ terms of $\{a_n\}$. Find $S_{2016}$.

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