
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 that ${(1-2x)^{2016}}=a_{0}+a_{1}(x-2)+a_{2}(x-2)^{2}+\cdots+a_{2015}(x-2)^{2015}+a_{2016}(x-2)^{2016}$ $(x\in\mathbb{R})$, find the value of $a_{1}-2a_{2}+3a_{3}-4a_{4}+\cdots+2015a_{2015}-2016a_{2016}$.

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