
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
Certain tickets are numbered as follows:  $1, 2, 3, \dots, N $ . Exactly half of the tickets have the digit  $ 1$  on them. If   $N$  is a three-digit number, determine all possible values ​​of  $N $ .

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