
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 that $(2x-1)^{2013}=a\_0+a\_1x+a\_2x^2+...+a_{2013}x^{2013} (x\in R)$, find the value of $\frac{1}{2}+\frac{a\_2}{2^2a\_1}+\frac{a\_3}{2^3a\_1}+...+\frac{a_{2013}}{2^{2013}a\_1}$.

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