
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 \( \{a_{n}\} \) with the sum of the first \( n \) terms \( S_{n} = 2a_{n} - 1 \) for \( n = 1, 2, \cdots \), and the sequence \( \{b_{n}\} \) satisfies \( b_{1} = 3 \) and \( b_{k+1} = b_{k} + a_{k} \) for \( k = 1, 2, \cdots \). Find the sum of the first \( n \) terms of the sequence \( \{b_{n}\} \).

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