
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
(I) Given an arithmetic sequence $\{a_n\}$, where $a_1+a_3+a_5=21$, find the sum of the first five terms of the sequence, $S_5$.
(II) Given a geometric sequence $\{a_n\}$, where $a_1=2$, $a_n=64$, and the common ratio $q=2$, find the sum of the sequence up to the nth term, $S_n$.

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