
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 with all positive terms $\{a_n\}$ has a first term $a_{1}=8$, and $2a_{1}$, $a_{3}$, $3a_{2}$ form an arithmetic sequence.

(i) Find the general formula for the term $a_n$ of the sequence $\{a_n\}$;

(ii) For the sequence $\{b_n\}$, given $b_n = \frac{1}{n\log_{2}{a_n}}$, find the sum of the first $n$ terms, $S_n$.

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