
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 geometric sequence $\left\{{a}_{n}\right\}$ where all terms are positive, it is known that ${a}_{2}{a}_{4}=16$ and ${a}_{6}=32$. Let ${b}_{n}={a}_{n}+{a}_{n+1}$. Find the sum of the first 5 terms of the sequence $\left\{{b}_{n}\right\}$, denoted as ${S}_{5}$.

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