
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
João has a deck with 52 cards numbered from 1 to 52. A set of three cards is called "lucky" if the sum of the digits on each card is the same. What is the minimum number of cards João must draw from the deck, without looking, such that among the cards he has drawn, there are necessarily three cards that form a "lucky" set of cards?

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