
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
In a geometric progression whose terms are positive, any term equals the sum of the next three following terms. Determine the common ratio.
**A)** \( 1 \)  
**B)** \( \frac{-1 + \sqrt[3]{19+3\sqrt{33}} + \sqrt[3]{19-3\sqrt{33}}}{3} \)  
**C)** \( \frac{\sqrt{5}-1}{2} \)  
**D)** \( \frac{1-\sqrt{5}}{2} \)  
**E)** \( \frac{2}{\sqrt{5}} \)

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