
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
The numbers $\log(a^4b^8)$, $\log(a^7b^{14})$, and $\log(a^{11}b^{19})$ are the first three terms of an arithmetic sequence. Determine the value of $n$ if the $15^\text{th}$ term of the sequence is $\log(a^2b^n)$.
A) 130
B) 134
C) 136
D) 138
E) 140

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