
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
Find the common ratio \( r \) of the geometric progression for which the terms are of the form \( a+x \), \( b+x \), and \( c+x \) where \( a = 30 \), \( b = 80 \), and \( c = 160 \). Determine \( x \) such that these modified terms form a true geometric sequence.
A) \( \frac{7}{4} \)
B) \( \frac{8}{5} \)
C) \( \frac{3}{2} \)
D) \( \frac{10}{7} \)

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