
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 $(1-2x)^{2016} = a_{0} + a_{1}x + \ldots + a_{2016}x^{2016}$ ($x \in \mathbb{R}$), calculate $\frac{a_{1}}{2} + \frac{a_{2}}{2^{2}} + \ldots + \frac{a_{2016}}{2^{2016}}$.

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