
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 progression with the sum of its first $n$ terms denoted as $S\_n$. It is known that $a\_3+a\_9=24$ and $S\_5=30$.
(1) Find the general term formula of the sequence $\{a\_n\}$;
(2) Find the sum of the first $n$ terms, denoted as $T\_n$, of the sequence $\{\frac{1}{a\_n \cdot a\_{n+2}}\}$.

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