
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 magician and their assistant are about to perform a trick. The spectator writes a sequence of $N$ digits on a board. The magician's assistant covers two neighboring digits with a black circle. Then the magician enters. The task for the magician is to guess both covered digits (and the order in which they are placed). What is the smallest value of $N$ where the magician can make an agreement with the assistant such that the trick always succeeds?

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