
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 the sum of the first $n$ terms of the sequence $\{a\_n\}$ is $S\_n$, and $S_n + \frac{1}{2}a\_n = 1 (n \in \mathbb{N}^*)$.

(1) Find the general term formula of the sequence $\{a\_n\}$.

(2) Let $b_n = \log_{\frac{1}{3}} \frac{1-S_n}{3} (n \in \mathbb{N}^*)$, and $T_n = \frac{1}{b_1 b_2} + \frac{1}{b_2 b_3} + ... + \frac{1}{b_n b_{n+1}}$, find $T_n$.

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