
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 mid-term exam results of Chinese, Mathematics, and English for a certain class are as follows: There are 18 students who have achieved excellence in at least one course; 9 students have achieved excellence in Chinese, 11 in Mathematics, and 8 in English; 5 students have achieved excellence in both Chinese and Mathematics, 3 in both Mathematics and English, and 4 in both Chinese and English. 
(1) How many students have achieved excellence in at least one of the courses, Chinese or Mathematics?
(2) How many students have achieved excellence in all three courses, Chinese, Mathematics, and English?

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