
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 $(x+1)^2(x+2)^{2016} = a_0 + a_1(x+2)^1 + a_2(x+2)^2 + \cdots + a_{2018}(x+2)^{2018}$, find the value of $\frac{a_1}{2^1} + \frac{a_2}{2^2} + \frac{a_3}{2^3} + \cdots + \frac{a_{2018}}{2^{2018}}$.

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