
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 arithmetic sequence {a<sub>n</sub>}, where a<sub>4</sub> = 9, a<sub>8</sub> - a<sub>3</sub> = 10. The sequence {b<sub>n</sub>} is a geometric sequence, with b<sub>2</sub> = a<sub>3</sub> - 3, b<sub>5</sub> = 6a<sub>2</sub> + 2.
(1) Find the general term formula a<sub>n</sub> and the sum of the first n terms S<sub>n</sub> for the sequence {a<sub>n</sub>}.
(2) Find the general term formula b<sub>n</sub> and 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}
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