
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
In the sequence $\{ a\_n \}$, $a\_1 = 1$, and when $n \geqslant 2$, the sum of its first $n$ terms, $S\_n$, satisfies $S\_n^2 = a\_n(S\_n - \frac{1}{2})$.
(1) Find $a\_n$;
(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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