
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 the geometric sequence $\{a\_n\}$ that satisfies $a\_1 = 2$ and $a\_2 \cdot a\_4 = a\_6$.
1. Find the general formula for the $n$-th term of the sequence.
2. Let $b\_n = \frac{1}{\log_{2}{a_{2n - 1}} \cdot \log_{2}{a_{2n + 1}}}$. Find the sum of first $n$ terms, denoted as $S\_n$, for the sequence $\{b\_n\}$.

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