
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 level magic and spellcasting competition consists of 5 spells. Out of 100 young wizards who participated in the competition:

- 95 performed the 1st spell correctly
- 75 performed the 2nd spell correctly
- 97 performed the 3rd spell correctly
- 95 performed the 4th spell correctly
- 96 performed the 5th spell correctly.

What is the minimum number of students who could have performed exactly 4 out of the 5 spells correctly under the given conditions?

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