
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 that all terms of the geometric sequence $\left\{ a_n \right\}$ are positive numbers not equal to $1$, and the sequence $\left\{ b_n \right\}$ satisfies $b_n = \lg a_n$, $b_3=18$, $b_6=12$, then the maximum value of the sum of the first $n$ terms of the sequence $\left\{ b_n \right\}$ is $\boxed{\text{C: }132}$.

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