
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 a geometric sequence, and $S_n$ is the sum of the first $n$ terms, it is known that $S_3 = \frac{7}{2}$ and $S_6 = \frac{63}{2}$.  
(1) Find the general formula for the sequence $\{a_n\}$.  
(2) Calculate the sum of the first 8 terms.

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