
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 $\{a\_n\}$, where $a\_2 + a\_6 = 6$ and $S\_n$ represents the sum of its first $n$ terms, with $S\_5 = \frac{35}{3}$.

(1) Find the general term formula for the sequence $\{a\_n\}$.

(2) Let $\{b\_n\} = \frac{1}{a_{n-1}a\_n}$ for $n \geq 2$, $b\_1 = 3$, and $S\_n = b\_1 + b\_2 + \dots + b\_n$. Find the value of $S\_{19}$.

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