
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 $\{a\_n\}$ is an increasing arithmetic sequence, where $a\_1$ and $a\_2$ are the roots of the equation $x^2 - 3x + 2 = 0$.
(I) Find the general term formula for the sequence $\{a\_n\}$;
(II) Find the sum of the first $n$ terms, denoted as $S_n$, for the sequence $\{\frac{1}{a\_n a_{n+1}}\}$.

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