
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 decreasing geometric sequence, where $q$ is the common ratio, and $S_n$ is the sum of the first $n$ terms. Given that $\{a_1, a_2, a_3\} \subseteq \{-4, -3, -2, 0, 1, 2, 3, 4\}$, find the value of $$\frac {S_{8}}{1-q^{4}}$$.

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