
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 the positive sequence $\{a_n\}$, where $a_1=2$, $a_2=1$, and $\frac {a_{n-1}-a_{n}}{a_{n}a_{n-1}}= \frac {a_{n}-a_{n+1}}{a_{n}a_{n+1}}(n\geqslant 2)$, find the value of the 2016th term of this sequence.

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