
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 respective common ratios $p$ and $r$. It is given that $$a_3-b_3=5(a_2-b_2).$$ Determine the sum of the common ratios of the two sequences.

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