
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 $(1-2x)^{2016}=a_0+a_1(x-2)+a_2(x-2)^2+...+a_{2015}(x-2)^{2015}+a_{2016}(x-2)^{2016}(x∈R)$, find the value of $a_1-2a_2+3a_3-4a_4+...+2015a_{2015}-2016a_{2016}$.

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