
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 {a<sub>n</sub>} is an arithmetic sequence with a first term of 19 and a common difference of -2, and S<sub>n</sub> is the sum of the first n terms of {a<sub>n</sub>}.
(Ⅰ) Find the nth term a<sub>n</sub> and S<sub>n</sub>;
(Ⅱ) If {b<sub>n</sub> - a<sub>n</sub>} is a geometric sequence with a first term of 1 and a common ratio of 3, find the nth term formula for the sequence {b<sub>n</sub>} and its sum of the first n terms T<sub>n</sub>.

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