
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 $m$, $a_1, a_2, a_3$ and $n$, $b_1, b_2, b_3$ be nonconstant arithmetico-geometric sequences where the terms increase by multiplying by a common ratio and adding a common difference (`$50, 55p + 5, 60p^2 + 10p` and similarly for $b$`). If $a_3 - b_3 = 3(a_2 - b_2)$, determine the sum of the common ratios of the two sequences.

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