
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 $\log(a^5b^7)$, $\log(a^{11}b^{17})$, and $\log(a^{19}b^{29})$ are the first three terms of an arithmetic sequence. What is the value of $n$ if the $10^\text{th}$ term of this sequence is $\log(b^n)$?
A) 144
B) 150
C) 156
D) 160
E) 170

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