
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
Let $S_{n}$ be the sum of the first $n$ terms of the sequence ${a_{n}}$, with $a_{1}=1$ and $S_{n}^2 = a_{n}(S_{n} - \frac{1}{2}), (n \geqslant 2)$.
(1) Find the general term ${a_{n}}$;
(2) Let $b_{n} = \frac{S_{n}}{2n+1}$, find the sum of the first $n$ terms of the sequence ${b_{n}}$, denoted as $T_{n}$.

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