
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 say that a positive integer N is *nice* if it satisfies the following conditions: $\bullet$  All of its digits are  $1$  or  $2$  $\bullet$  All numbers formed by  $3$  consecutive digits of  $N$  are distinct.
For example,  $121222$  is nice, because the  $4$  numbers formed by  $3$  consecutive digits of  $121222$ , which are  $121,212,122$  and  $222$ , are distinct. However,  $12121$  is not nice. What is the largest quantity possible number of numbers that a nice number can have? What is the greatest nice number there is?

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