
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
There is a sequence of numbers $a_{1}$, $a_{2}$, $a_{3}$, $a_{4}$, ..., $a_{n}$. Starting from the second number, each number is equal to the difference between $1$ and the reciprocal of the previous number. For example, if $a_{1}=3$, then $a_{2}=1-\frac{1}{3}=\frac{2}{3}$, $a_{3}=1-\frac{3}{2}=-\frac{1}{2}$, ... . Calculate the value of $a_{2016}$ when $a_{1}=2$.

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