
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
Bernardo picks a three-digit number $N$ and writes its base-3 and base-4 representations. Later, LeRoy, treating these numbers as base-10 integers, multiplies them instead of adding them and gets a number $M$. How many such $N$ are there such that the two rightmost digits of $M$ are the same as those of $3N$?
A) 15
B) 20
C) 25
D) 30
E) 35

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