
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
Divide 23 cards, each labeled with numbers 1 to 23, into three piles. It is known that the average numbers of the three piles are 13, 4, and 17, respectively. What is the minimum number of cards in the pile with an average number of 13?

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