
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 
$$(x+1)^{2}(x+2)^{2016}=a_{0}+a_{1}(x+2)+a_{2}(x+2)^{2}+\dots+a_{2018}(x+2)^{2018},$$ 
find the value of 
$$\frac{a_{1}}{2}+\frac{a_{2}}{2^{2}}+\frac{a_{3}}{2^{3}}+\dots+\frac{a_{2018}}{2^{2018}}.$$

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