
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 $\{a\_n\}$ where the sum of the first $n$ terms, $S\_n$, and the $n$-th term, $a\_n$, satisfy $S\_n=\frac{1}{2}(1-a\_n)$.
(1) Find the general term formula for the sequence $\{a\_n\}$;
(2) Let $f(x)=\log_{\frac{1}{3}}x$, $b\_n=f(a\_1)+f(a\_2)+...+f(a\_n)$, and $T\_n=\frac{1}{b\_1}+\frac{1}{b\_2}+\frac{1}{b\_3}+...+\frac{1}{b\_n}$. Find the range of $T\_n$.

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