
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 $\{a\_n\}$ with the sum of its first $n$ terms denoted as $S\_n$, and $a\_n + S\_n = 1 (n \in \mathbb{N}^*)$.

(1) Find the general term formula for the sequence $\{a\_n\}$;

(2) If sequence $\{b\_n\}$ satisfies $b\_n = 3 + \log\_4{a\_n}$, and $T\_n = |b\_1| + |b\_2| + ... + |b\_n|$, find $T\_n$.

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