
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
There are 30 students in a class. In each lesson, Miss Blackwick, the English teacher, asks one of three selected students to recite a page from an English-French dictionary, and among these selected students, there is always one of the ten students who were asked in the previous lesson. One of the students, a notorious slacker, decided that he will only prepare the homework for the next lesson if he was not asked in the previous one.

“What are my chances,” he wonders, “of learning the lesson in vain or being scolded by Miss Blackwick for not having learned the lesson?”

Clarify his doubts.

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