
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 three digits in its base ten representation is chosen at random. Calculate the probability that $\log_3 N$ is an integer.
A) $\frac{1}{300}$   
B) $\frac{1}{225}$   
C) $\frac{2}{900}$   
D) $\frac{1}{900}$   
E) $\frac{1}{450}$

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