
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 the geometric sequence $\{a\_n\}$ has a common ratio of $q (0 < q < 1)$, and the sum of its first $n$ terms is $S\_n$. If $a\_1 = 4a\_3a\_4$, and the arithmetic mean between $a\_6$ and $\frac{3}{4}a\_4$ is $a\_5$, find $S\_6 = \_\_\_\_\_\_$.

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