
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
For positive integers $n$, define $g(n)$ to return the smallest positive integer $k$ such that $\frac{1}{k}$, when expressed in base $6$, has exactly $n$ digits after the radix point. Determine the number of positive integer divisors of $g(2023)$.

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