
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 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 all $n \in \mathbb{N}^*$, find the value of $b\_{2016}$.

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