
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. Pythagoras has $15$ students, Ms. Lovelace has $12$ students, and Mr. Euler has $10$ students, and $3$ students are enrolled in both Mr. Pythagoras's and Ms. Lovelace's classes, determine the total number of unique mathematics students at Euclid Middle School taking the contest.

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