
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 certain geometric progression with positive terms, any term minus the next term equals half the sum of the next two terms. If the first term is $a$ and the common ratio is $r$, determine the value of $r$.
**A** $\frac{\sqrt{17} - 3}{2}$
**B** $\frac{-\sqrt{17} - 3}{2}$
**C** $\sqrt{2}$
**D** $2$
**E** $\frac{1}{2}$

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