
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 $\{an\}$, $a1=1$, and when $n\geqslant 2$, the sum of its first $n$ terms $Sn$ satisfies $S\\rlap{\_{n}}{^{2}}=an\\left( \\left. S\_{n}- \\dfrac{1}{2} \\right. \\right)$.

(1) Find the expression for $Sn$;

(2) If $bn= \\dfrac{S\_{n}}{2n+1}$, find the sum of the first $n$ terms of the sequence $\{bn\}$, denoted as $Tn$.

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