
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 a sequence {a<sub>n</sub>} with the sum of the first n terms denoted as S<sub>n</sub>, and a<sub>1</sub> + √(S<sub>n</sub>) = n + 1,

1. Find S<sub>n</sub> and a<sub>n</sub>.
2. If b<sub>n</sub> = (-1)^(n-1) • (a<sub>n+1</sub> / (S<sub>n</sub> + n)), and the sum of the first n terms of {b<sub>n</sub>} is T<sub>n</sub>, find T<sub>n</sub>.

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