
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 $\{a_n\}$ that satisfies $a_3=2$, and the sum of the first 3 terms $S_3 = \frac{9}{2}$.

(1) Find the general formula for $\{a_n\}$.    
(2) Let $\{b_n\}$ be a geometric sequence that satisfies $b_1=a_1$, and $b_4=a_{15}$. Find the sum of the first $n$ terms of $\{b_n\}$, denoted by $T_n$.

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