
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 sequence with a non-zero common difference, $S_n$ represents the sum of the first $n$ terms of the sequence $\{a\_n\}$, $S_5 = 20$, and $a_1$, $a_3$, $a_7$ form a geometric sequence.

(1) Find the general term formula for the sequence $\{a\_n\}$.
(2) If $b_{n+1} = b_n + a_n$, and $b_1 = 1$, find the sum of the first $n$ terms, $T_n$, for the sequence $\{ \frac{1}{b_n} \}$.

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