
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 $(1-2x)^{2013} = a_0 + a_1x + \ldots + a_{2013}x^{2013}$ ($x \in \mathbb{R}$), then $\frac{a_1}{2} + \frac{a_2}{2^2} + \ldots + \frac{a_{2013}}{2^{2013}} = \boxed{\text{\_\_\_\_\_\_}}$.

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