
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 arithmetic sequence, and the sequence $\{b\_n\}$ satisfies $b\_n=a\_n+n$. If $b\_2$, $b\_5$, $b\_11$ form a geometric sequence, and $b\_3=a\_6$.

1. Find $a\_n$ and $b\_n$.
2. Find the sum of the first $n$ terms, $S\_n$, of the sequence $\{ \frac {1}{a\_n b\_n} \}$.

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