
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 an arithmetic sequence $\{a_{n}\}$ where the sum of the first n terms is $S_{n}$, and it satisfies $a_{n} > 0$, $q > 1$, $a_{3} + a_{5} = 20$, and $a_{2}a_{6} = 64$, calculate the value of $S_{5}$.

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