
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
On \( n \) cards, numbers are written on different sides: on the 1st card: 0 and 1; on the 2nd: 1 and 2; ..., on the \( n \)-th: \( n - 1 \) and \( n \). One person takes several cards from the stack and shows the second person one side of each of them. Then they take another card from the stack and also show one side. Indicate all cases in which the second person can determine the number written on the back of the last card shown.

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