
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 a sequence $\{a\_n\}$ with its first $n$ terms sum $S\_n$. It is known that $a\_1=2$ and $S\_n=\frac{n+2}{3}a\_n \, (n \in \mathbb{N}^*)$.

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

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