
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
What is the least number  $N$  of 4-digits numbers compiled from digits  $1,2,3,4,5,6,7,8$  you need to choose, that for any two different digits, both of this digits are in
a) At least in one of chosen  $N$  numbers?
b)At least in one, but not more than in two of chosen  $N$  numbers?

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