
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
Let {a_n} be a positive geometric sequence with the sum of its first n terms denoted by S_n, and such that $$\frac{a_{n+1}}{a_n} < 1$$. If a_3 + a_5 = 20 and a_2 \cdot a_6 = 64, find the value of S_6.

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