
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 $\{a\_n\}$, $(n\geqslant 1,n\in N)$ that satisfies $a\_1=2$, $a\_2=6$, and $(a_{n+2}-a_{n+1})-(a_{n+1}-a_{n})=2$, if $[x]$ represents the largest integer not exceeding $x$, then the value of $[ \frac {2016}{a_{1}}+ \frac {2016}{a_{2}}+…+ \frac {2016}{a_{2016}}]=$\_\_\_\_\_\_.

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