
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 $(1-2x)^{2014}=a\_0+a\_1x+...+a_{2014}x^{2014}$, then $\frac{a\_1}{2}+\frac{a^2}{2^2}+...+\frac{a_{2014}}{2^{2014}}=$ _____ .

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