
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 a geometric sequence of positive numbers $\{a_n\}$, where $S_n$ is the sum of the first $n$ terms of $\{a_n\}$, and $a_2 = \frac{1}{4}, S_3 = 7a_3$.  
(1) Find the general formula for $\{a_n\}$.  
(2) If the sequence $\{b_n\}$ satisfies $b_n = \frac{n}{a_n}$, find the sum of the first $n$ terms of $\{b_n\}$, denoted as $T_n$.

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