
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 \\({{\\left( x+1 \\right)}^{2}}{{\\left( x+2 \\right)}^{2016}}={{a}_{0}}+{{a}_{1}}\\left( x+2 \\right)+{{a}_{2}}{{\\left( x+2 \\right)}^{2}}+...+{{a}_{2018}}{{\\left( x+2 \\right)}^{2018}}\\), find the value of \\(\dfrac{{a}_{1}}{2}+\dfrac{{a}_{2}}{{2}^{2}}+\dfrac{{a}_{3}}{{2}^{3}}+...+\dfrac{{a}_{2018}}{{2}^{2018}}\\).

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