
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
In a class, the number of students who excel in mathematics, physics, and chemistry are 30, 28, and 25 respectively. The number of students who excel in both mathematics and physics, physics and chemistry, and mathematics and chemistry are 20, 16, and 17 respectively. The number of students who excel in all three subjects, mathematics, physics, and chemistry, is 10. How many students excel in at least one of the subjects, mathematics or physics? How many students excel in at least one of the three subjects, mathematics, physics, or chemistry?

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