
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
Let \(k, a_2, a_3\) and \(k, b_2, b_3\) be nonconstant geometric sequences with different common ratios. If
\[
a_3 - b_3 = 3(a_2 - b_2),
\]
then what is the sum of the common ratios of the two sequences?

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