
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
In the sequences {a<sub>n</sub>} and {b<sub>n</sub>}, for all n belonging to the set of positive integers, $$a_{n}=2^{n}$$, and a<sub>n</sub>, b<sub>n</sub>, a<sub>n+1</sub> form an arithmetic sequence. Find the sum of the first n terms, S<sub>n</sub>, of the sequence {b<sub>n</sub>}.

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