
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
In a certain school, there are 5000 students. Each student is assigned an ID number from 0001 to 5000. No two students can have the same ID number. If a student is selected uniformly at random, what is the probability that the ID number of the student does not contain any 2s among its digits?

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