
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 $\{a_n\}$ with a common ratio $q>0$ and the sum of the first $n$ terms denoted as $S_n$. If $2a_3$, $a_5$, and $3a_4$ form an arithmetic sequence, and $a_2a_4a_6=64$, then $a_n=$ ______, $S_n=$ ______.

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