
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
It is known that the number of student volunteers in grades A, B, and C of a certain school are $240$, $160$, and $160$, respectively. By using stratified sampling, $7$ students are to be selected to participate in a volunteer activity at a nursing home.  
(Ⅰ) How many volunteers should be selected from each of the grades A, B, and C?  
(Ⅱ) Let the $7$ selected students be denoted as $A$, $B$, $C$, $D$, $E$, $F$, and $G$. If $2$ students are randomly selected to take on the sanitation work at the nursing home,  
(i) List all possible outcomes of the selection using the given letters;  
(ii) Let $M$ be the event that the $2$ selected students are from the same grade. Calculate the probability of event $M$ occurring.

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