
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
In the geometric sequence $\{a_n\}$, the common ratio $q > 1$, and it's given that $a_1 + a_4 = 9$ and $a_2 \cdot a_3 = 8$.
(1) Find the values of $a_1$ and $q$.
(2) Calculate the sum of the first 6 terms of the sequence, $S_6$.

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