
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 bank serves a million clients, and Ostap Bender knows the list of these clients. Each client has a unique six-digit PIN code. On each move, Ostap Bender can choose a client he has not yet chosen and peek at the digits of the code in any $N$ positions (he can choose different positions for different clients). Ostap wants to find out the PIN code of millionaire Koreiko. What is the smallest number, $N$, that guarantees he can do this?

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