
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 $\{a_{n}\}$, $a_{1} > 0$, $n∈N^{*}$, and $a_{5}-a_{4}=8$, the geometric mean of $a_{2}$ and $a_{8}$ is $16$.

1. Find the general term formula of the sequence $\{a_{n}\}$;
2. Let $b_{n}=\log_{4}a_{n}$, and $S_{n}$ denote the sum of the first $n$ terms of the sequence $\{b_{n}\}$. Find the sum $\frac{1}{S_{2}}+\frac{1}{S_{3}}+...+\frac{1}{S_{n}}$.

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