
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
In a deck of 52 cards, each player makes one cut. A cut consists of taking the top $N$ cards and placing them at the bottom of the deck without changing their order.

- First, Andrey cut 28 cards,
- then Boris cut 31 cards,
- then Vanya cut 2 cards,
- then Gena cut an unknown number of cards,
- then Dima cut 21 cards.

The last cut restored the original order. How many cards did Gena cut?

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