
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 an arithmetic sequence $\{a\_n\}$ with a common difference of $2$, let $S\_n$ denote the sum of its first $n$ terms. If $a\_1$, $S\_2$, and $S\_4$ form a geometric sequence:

1. Find the general term formula for the sequence $\{a\_n\}$.
2. Let $b\_n = \frac{2}{a\_n \cdot a_{n+1}}$ for all positive integers $n$. Find the sum $T\_n$ of the first $n$ terms of the sequence $\{b\_n\}$.

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