
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
The set  $X$  of  $N$  four-digit numbers formed from the digits  $1,2,3,4,5,6,7,8$  satisfies the following condition:


*for any two different digits from  $1,2,3,4,,6,7,8$  there exists a number in  $X$  which contains both of them.*

Determine the smallest possible value of  $N$ .

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