
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]


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In a high school, each student has at least one excellent score in either Chinese or English. There are 200 students with excellent Chinese scores and 150 students with excellent English scores. If a random student is selected from the senior students, the probability that this student is excellent in both Chinese and English is $\frac{1}{6}$. A stratified sampling method is used to select 6 students to discuss Chinese and English learning issues, based on the categories of excellence in Chinese not English, excellence in English not Chinese, and excellence in both. Among the 6 selected students, let there be $a$ students who are excellent in Chinese not English, $b$ students who are excellent in English not Chinese, and $c$ students who are excellent in both Chinese and English.
(Ⅰ) Find the values of $a$, $b$, and $c$.  
(Ⅱ) If 2 students are then randomly selected from these 6 students, find the probability $P$ that both have excellent Chinese scores.

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