
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
The school plans to organize an autumn outing for the students. Each bus has 39 seats, and each public bus has 27 seats. There are 2 fewer buses than public buses. If all students and teachers take the buses, with 2 teachers per bus, there will be 3 extra seats. If they all take the public buses, with each public bus fully occupied and each having 1 teacher, there will be 3 extra teachers. Find the total number of teachers and the total number of students participating in this autumn outing.

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