
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
Let the sequence $\{a_n\}$ satisfy $a_1=2$, $a_2=6$, and $a_{n+2}-2a_{n+1}+a_n=2$. If $\lfloor x \rfloor$ represents the greatest integer not exceeding $x$, calculate $$\left\lfloor \frac{2017}{a_1} + \frac{2017}{a_2} + \ldots + \frac{2017}{a_{2017}} \right\rfloor.$$

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