
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 each term is positive, let $S\_n$ denote the sum of the first $n$ terms, and let $a\_1$ be the first term. Furthermore, $2$, $a\_n$, and $S\_n$ form an arithmetic sequence.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. If $b\_n = \log\_2 a\_n$ and $c\_n = \frac{1}{b\_n b_{n+1}}$, find the sum $T\_n$ of the first $n$ terms of the sequence $\{c\_n\}$.

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