
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 that the sequence $\{a_n\}$ is a geometric sequence with the first term of $1$, $S_n$ is the sum of the first $n$ terms of $\{a_n\}$, and $\frac{S_4}{S_8} = \frac{1}{17}$, determine the sum of the first 5 terms of the sequence $\{\frac{1}{a_n}\}$.

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