
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
The difference of an arithmetic progression is non-zero. The numbers, which are equal to the products of the first term with the second term, the second term with the third term, and the third term with the first term in the given order, form a geometric progression. Find its common ratio.

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