
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 the first term $a$ and common difference $b$, and the solution set of the inequality $ax^2 - 3x + 2 > 0$ is $(-\infty, 1) \cup (b, +\infty)$,
1. Find the general term formula for the sequence $\{a_n\}$.
2. Let sequence $\{b_n\}$ be such that $b_n = \frac {1}{a_{n}a_{n+1}}$, find the sum of the first $n$ terms $S_n$ of sequence $\{b_n\}$.

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