
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
A positive integer $N$ with four digits in its base ten representation is chosen at random, 
with each four-digit number having an equal chance of being chosen. The probability that $\log_3 N$ is an integer is to be determined.
**A** $\frac{1}{4500}$
**B** $\frac{2}{9000}$
**C** $\frac{1}{2250}$
**D** $\frac{1}{9000}$

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