
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 $a_1= \frac{1}{3}$, $a_2= \frac{2}{3}$, and $a_{n+2}-a_{n+1}=(-1)^{n+1}(a_{n+1}-a_{n})$ for $n\in\mathbb{N}^*$, the sum of the first $n$ terms of the sequence $\{a_n\}$ is denoted as $S_n$. Find the value of $S_{2017}$.

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