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

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