
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
Given that Mr. Euler teaches 12 students, Mrs. Fibonacci teaches 10 students, and Mr. Gauss teaches 11 students for a mathematics contest, and 3 students are taught by both Mr. Euler and Mrs. Fibonacci, find the total number of distinct students preparing for the contest.

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