
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 sequence $\left\{a_{n}\right\}$ with the sum of its first $n$ terms $S_{n}= 2a_{n} - 1$ for $n = 1, 2, \ldots$, and the sequence $\left\{b_{n}\right\}$ satisfying $b_{1} = 3$ and $b_{k+1} = a_{k} + b_{k}$ for $k = 1, 2, \ldots$, find the sum of the first $n$ terms of the sequence $\left\{b_{n}\right\}$.

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