
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
During the university entrance exams, each applicant is assigned a cover code consisting of five digits. The exams were organized by a careful but superstitious professor who decided to exclude from all possible codes (i.e., 00000 to 99999) those that contained the number 13, that is, the digit 3 immediately following the digit 1. How many codes did the professor have to exclude?

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