
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
Consider two nonconstant geometric sequences where $k, a_2, a_3$ follows the first sequence with a common ratio of $p$, and $k, b_2, b_3$ follows the second sequence with a common ratio of $r$. Given that 
$$a_3 - b_3 = 4(a_2 - b_2),$$
find the sum of the common ratios $p$ and $r$.

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