
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 the sequence $\{a\_n\}$, where $a\_1=1$ and the sum of the first $n$ terms $S\_n=\frac{n+2}{3}a\_n$.
(I) Find $a\_2$, $a\_3$, and the general formula for $\{a\_n\}$;
(II) Let $b\_n=\frac{1}{a\_n}$, find the sum of the first $n$ terms $T\_n$ for the sequence $\{b\_n\}$.

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