
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 two sequences $\{a_n\}$ and $\{b_n\}$ satisfying $a_1= \frac{1}{2}$, $a_n+b_n=1$, $b_{n+1}= \frac{b_n}{1-a_n^2}$, for $n\in\mathbb{N}_+$, find the value of $b_{2016}$.

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