
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
If $(1-2x)^{2011}=a_{0}+a_{1}x+\ldots+a_{2011}x^{2011}$ (x∈ℝ), then find the value of $\frac{a_{1}}{2}+\frac{a_{2}}{2^{2}}+\ldots+\frac{a_{2011}}{2^{2011}}$.

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