
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 a positive geometric sequence $\{a_{n}\}$, where $a_{1}=1$ and the sum of its first $n$ terms is $S_{n}$ $(n\in N_{+})$, if $\frac{1}{{{a_1}}}-\frac{1}{{{a_2}}}=\frac{2}{{{a_3}}}$, calculate $S_{5}$.

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