
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
Consider the sequence $\{a\_n\}(n\geqslant 1,n\in\mathbb{N})$ that satisfies $a\_1=2$, $a\_2=6$, and $a\_{n+2}-2a\_{n+1}+a\_n=2$. If $[x]$ represents the largest integer not exceeding $x$, then the value of $\left[\frac{2017}{a\_1}+\frac{2017}{a\_2}+...+\frac{2017}{a\_{2017}}\right]$ is \_\_\_\_\_\_.

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