
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 a sequence of positive numbers with a sum of the first n terms denoted as S<sub>n</sub>, and a<sub>1</sub> = 1, S<sub>n+1</sub><sup>2</sup> = S<sub>n</sub><sup>2</sup> + 1.
(1) Find the general formula for the sequence {S<sub>n</sub>}.
(2) Let b<sub>n</sub> = $\frac{(-1)^{n}}{a_{n}}$, find the sum of the first n terms, T<sub>n</sub>, of the sequence {b<sub>n</sub>}.

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