
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 $\{a\_n\}$ with a non-zero common difference, let $S\_n$ represent the sum of its first $n$ terms. The first term $a\_1$ is 2, and $a\_1$, $a\_2$, $a\_4$ form a geometric sequence.

(1) Find the general term formula for the sequence $\{a\_n\}$.

(2) If ${b\_n} = \frac{1}{S\_{n+1}}$, let $T\_n$ represent the sum of the first $n$ terms of the sequence $\{b\_n\}$. Find $T\_n$.

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