
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 arithmetic sequence $\{a\_n\}$ has a sum of its first $n$ terms denoted as $S\_n$, and $S\_5=4a\_3+6$. Also, $a\_2$, $a\_3$, $a\_9$ form a geometric sequence.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. If $a\_1 \neq a\_5$, find the sum of the first $n$ terms for the sequence $\{ \frac {1}{S\_n}\}$.

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