
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 Smurfs, and there are a total of 11 types of Smurfs. The box contains a sufficient number of Kinder Surprises, where no two of them have identical sets of three Smurfs. What is the minimum number of Kinder Surprises that need to be purchased so that after opening them, there is at least one of each of the 11 types of Smurfs?

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