
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
We want to choose telephone numbers for a city. The numbers have  $10$  digits and  $0$  isn’t used in the numbers. Our aim is: We don’t choose some numbers such that every  $2$  telephone numbers are different in more than one digit OR every  $2$  telephone numbers are different in a digit which is more than  $1$ . What is the maximum number of telephone numbers which can be chosen? In how many ways, can we choose the numbers in this maximum situation?

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