
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 sequence $\{a\_n\}$ has a sum of the first $n$ terms denoted by $S\_n$, with the first term $a\_1$ equal to 1, and that $1$, $a\_n$, $S\_n$ form an arithmetic sequence.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. The sequence $\{b\_n\}$ satisfies $b\_n = (\log\_2 a\_{2n+1}) \times (\log\_2 a\_{2n+3})$. Find the sum of the first $n$ terms of the sequence $\{\frac{1}{b\_n}\}$, denoted by $T\_n$.

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