
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
Among the applicants who passed the entrance exams to a technical university, the grades of "excellent" were received as follows: 48 people in mathematics, 37 people in physics, 42 people in literature, 75 people in mathematics or physics, 76 people in mathematics or literature, 66 people in physics or literature, and 4 people in all three subjects. How many applicants received only one "excellent" grade? Exactly two "excellent" grades? At least one "excellent" grade?

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