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

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