
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 an increasing sequence $\{a_n\}$ with $2017$ terms, and all terms are non-zero, $a_{2017}=1$. If two terms $a_i$, $a_j$ are arbitrarily chosen from $\{a_n\}$, when $i < j$, $a_j-a_i$ is still a term in the sequence $\{a_n\}$. Then, the sum of all terms in the sequence $S_{2017}=$ ______.

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