
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 $\{a\_n\}$ that satisfies $a\_5=3$ and the sum of the first 3 terms $S\_3$ is $\frac{9}{2}$.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. Find the sum of the first $n$ terms for the sequence $\{\frac{1}{a\_na\_{n+2}}\}$.

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