
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 $a= \frac {1}{\pi } \int_{ -2 }^{ 2 } (\sqrt {4-x^{2}} - e^x)dx$, if $(1-ax)^{2016} = b_0 + b_1x + b_2x^2 + \ldots + b_{2016}x^{2016}$ ($x \in \mathbb{R}$), calculate the value of $\frac {b_{1}}{2} + \frac {b_{2}}{2^{2}} + \ldots + \frac {b_{2016}}{2^{2016}}$.

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