
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 $\{a_n\}$ is a geometric sequence and let $S_n$ be the sum of its first $n$ terms, given that $a_2 \cdot a_3 = 8a_1$ and the arithmetic mean of $a_4$ and $2a_5$ is 20, calculate the value of $S_5$.

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