
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 that the sequence {a<sub>n</sub>} is a geometric sequence with the sum of the first n terms denoted as S<sub>n</sub>. If a<sub>1</sub> = 1, and S<sub>2</sub> + 1 is to S<sub>1</sub> + 1 as S<sub>3</sub> + 1 is to their geometric mean:

1. Find the general term formula for the sequence {a<sub>n</sub>}.
2. If b<sub>n</sub> = n • a<sub>n</sub>, find the sum of the first n terms, T<sub>n</sub>, for the sequence {b<sub>n</sub>}.

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