
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
If there exists a geometric sequence $\{a\_n\}$ such that $a\_1(a\_2 + a\_3) = 6a\_1 - 9$, find the maximum value of the common ratio $q$.
A) $\frac{1 + \sqrt{5}}{4}$
B) $\frac{1 + \sqrt{5}}{2}$
C) $\frac{-1 + \sqrt{5}}{4}$
D) $\frac{-1 + \sqrt{5}}{2}$

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