
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, satisfying $(a_1 + a_2 + a_3 = 21)$, and $a_1$, $a_6a_{12}$ form a geometric sequence.

(1) Find the general term formula for $\{a_n\}$;
(2) If the sequence $\{b_n\}$ satisfies $\frac{1}{b_{n+1}} - \frac{1}{b_n} = a_n (n \in \mathbb{N}^*)$, and $(b_1 = \frac{1}{3})$, find the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted as $T_n$.

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