
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
Each Kinder Surprise contains exactly 3 different gnomes, and there are 12 types of gnomes in total. The box contains a sufficient number of Kinder Surprises, and no two of them contain the same set of three gnomes. What is the minimum number of Kinder Surprises that need to be purchased to ensure that, after opening them, there is at least one of each of the 12 types of gnomes?

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