
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 $(2x-1)^{2015} = a_{0} + a_{1}x + a_{2}x^{2} + \ldots + a_{2015}x^{2015}$ ($x \in \mathbb{R}$), evaluate the expression $\frac {1}{2}+ \frac {a_{2}}{2^{2}a_{1}}+ \frac {a_{3}}{2^{3}a_{1}}+\ldots+ \frac {a_{2015}}{2^{2015}a_{1}}$.

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