
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 $(1-2x)^{2017} = a_0 + a_1(x-1) + a_2(x-1)^2 + \ldots + a_{2016}(x-1)^{2016} + a_{2017}(x-1)^{2017}$ ($x \in \mathbb{R}$), find the value of $a_1 - 2a_2 + 3a_3 - 4a_4 + \ldots - 2016a_{2016} + 2017a_{2017}$.

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