
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 $(1-2x)^{2014} = a_0 + a_1x + a_2x^2 + \ldots + a_{2014}x^{2014}$ ($x \in \mathbb{R}$), then the value of $a_0 + \frac{1}{2}a_1 + \frac{1}{2^2}a_2 + \frac{1}{2^3}a_3 + \ldots + \frac{1}{2^{2014}}a_{2014}$ is \_\_\_\_\_\_.

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