
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 a sequence $\left\{a_{n}\right\}$ with the partial sum $S_{n}=2 a_{n}-1$ for $n=1,2,\cdots$, and another sequence $\left\{b_{n}\right\}$ that satisfies the conditions $b_{1}=3$ and $b_{k+1}=a_{k}+b_{k}$ for $k=1,2,\cdots$. Find the partial sum of the sequence $\left\{b_{n}\right\}$.

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