
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
Given the sequence of logarithmic terms is arithmetic with a common difference, the difference between the first and second terms is $\log(a^5b^{12}) - \log(a^3b^7) = \log(a^2b^5)$, the difference between the second and third terms is $\log(a^8b^{15}) - \log(a^5b^{12}) = \log(a^3b^3)$. Determine the common difference of the arithmetic sequence.

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