
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
A deck of 54 cards is divided into several piles by a magician. An audience member writes a natural number on each card equal to the number of cards in that pile. The magician then shuffles the cards in a special way and redistributes them into several piles. The audience member again writes a natural number on each card equal to the number of cards in the new pile. This process continues. What is the minimum number of times this process needs to be performed so that the (unordered) array of numbers written on the cards becomes unique for each card?

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