
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]


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Consider the sequence $\{a\_n\}$ that satisfies $(a\_1=1,a_{n+1}=a\_n+n+1\,(n∈ℕ^∗) )$.

(1) Find the general formula for the sequence $\{a\_n\}$;
(2) If the sum of the first $n$ terms of the sequence $\{\frac{1}{a\_n}\}$ is denoted by $T\_n$, find $T\_n$.

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