
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
There are six cards, each marked with the numbers 0, 1, 2, 4, 6, and 9, respectively. The cards with 6 and 9 can be used interchangeably (6 can be flipped to represent 9). By selecting any three cards to form a three-digit number, the number of three-digit numbers whose digits sum to a multiple of 3 is $\boxed{40}$.

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