
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
Vasya needs to write one digit on each face of several cubes in such a way that any ordered combination of three digits from 000 to 999 inclusive can be obtained by selecting some three different cubes and placing them with suitable faces up in the correct order. Note that the digits 6 and 9 are not considered interchangeable when rotated by 180 degrees. What is the minimum number of cubes that Vasya must use?

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