
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
Volodya wants to make a set of cubes of the same size and write one digit on each face of every cube so that it is possible to form any 30-digit number from these cubes. What is the smallest number of cubes he needs for this? (Digits 6 and 9 do not turn into each other when flipped.)

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