
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 an arithmetic sequence {a<sub>n</sub>} with the sum of the first n terms denoted as S<sub>n</sub>, it is known that a<sub>1</sub> + a<sub>2</sub> = 0 and S<sub>5</sub> = 15.

1. Find a<sub>n</sub>.
2. If sequence {b<sub>n</sub>} satisfies the conditions: b<sub>1</sub> = a<sub>2</sub> and nb<sub>n+1</sub> + (a<sub>n</sub> + 2)b<sub>n</sub> = a<sub>3n+1</sub>b<sub>n</sub>, find the sum of the first n terms of sequence {b<sub>n</sub>}, denoted as T<sub>n</sub>.

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