
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)^{2009}=a_{0}+a_{1}x+\ldots+a_{2009}x^{2009} (x \in \mathbb{R})\\), then the value of \\( \frac {a_{1}}{2}+ \frac {a_{2}}{2^{2}}+\ldots+ \frac {a_{2009}}{2^{2009}}\\) is \_\_\_\_\_\_.

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