
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
A geometric sequence $\{a_n\}$ satisfies $a_3 + a_4 = 12$, $a_1a_6 = 32$, and the common ratio $q > 1$.
(1) Find the general formula for the sequence $\{a_n\}$.
(2) If the sum of the first $n$ terms of the sequence $S_n = 63$, find the value of $n$.

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