
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
Determine, if we shuffle 52 cards as described in the Szalonpóker article, after how many shuffles the original order is restored. Solve this problem also in the case when we start the shuffle with the bottom card of the right-hand pile, meaning the card originally in the 26th position becomes the bottom card.

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