
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 the sequences $\left\{a_{n}\right\}$, $\left\{b_{n}\right\}$ with $a_1=b_1=2$, $a_{n+1}-a_{n}=\dfrac{b_{n+1}}{b_{n}}=2$ for all $n\in N^{*}$, determine the sum of the first $n$ terms of the sequence $\left\{b_{n}\right\}$.

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