
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 its first $n$ terms sum $S\_n$, the first term $a\_1$, and the relation $\frac{1}{2}$, $a\_n$, $S\_n$ forming an arithmetic sequence.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. 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 $\{\frac{1}{b\_n}\}$.

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