
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 $\{a_n\}$ have a sum of the first $n$ terms denoted by $S_n$, with $a_1=2$. If $S_{n+1}= \dfrac {n+2}{n}S_{n}$, then the sum of the first $2016$ terms of the sequence $\left\{ \dfrac {1}{a_{n}a_{n+1}}\right\}$ equals \_\_\_\_\_\_.

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