
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 all terms are positive, the sum of the first $n$ terms is $S\_n$, the first term is $a\_1$, and $\frac{1}{2}$, $a\_n$, $S\_n$ form an arithmetic sequence.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. If $a\_n^2 = (\frac{1}{2})^{b\_n}$, let $c\_n = \frac{b\_n}{a\_n}$, find the sum of the first $n$ terms $T\_n$ for the sequence $\{c\_n\}$.

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