
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
Suppose that {a<sub>n</sub>} is a geometric sequence with the first term 1 and a common ratio of 3.
(I) Find the general term formula for {a<sub>n</sub>} and the sum of the first n terms S<sub>n</sub>.
(II) Given that {b<sub>n</sub>} is an arithmetic sequence, T<sub>n</sub> is the sum of the first n terms, and b<sub>1</sub> = a<sub>2</sub>, b<sub>3</sub> = a<sub>1</sub> + a<sub>2</sub> + a<sub>3</sub>, find T<sub>20</sub>.

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